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	<id>https://wikisofia.cz/w/index.php?action=history&amp;feed=atom&amp;title=Lindenbaum-Tarsk%C3%A9ho_algebry</id>
	<title>Lindenbaum-Tarského algebry - Historie editací</title>
	<link rel="self" type="application/atom+xml" href="https://wikisofia.cz/w/index.php?action=history&amp;feed=atom&amp;title=Lindenbaum-Tarsk%C3%A9ho_algebry"/>
	<link rel="alternate" type="text/html" href="https://wikisofia.cz/w/index.php?title=Lindenbaum-Tarsk%C3%A9ho_algebry&amp;action=history"/>
	<updated>2026-04-12T04:05:20Z</updated>
	<subtitle>Historie editací této stránky</subtitle>
	<generator>MediaWiki 1.33.0</generator>
	<entry>
		<id>https://wikisofia.cz/w/index.php?title=Lindenbaum-Tarsk%C3%A9ho_algebry&amp;diff=9445&amp;oldid=prev</id>
		<title>HonzaB: /* Vlastnosti */</title>
		<link rel="alternate" type="text/html" href="https://wikisofia.cz/w/index.php?title=Lindenbaum-Tarsk%C3%A9ho_algebry&amp;diff=9445&amp;oldid=prev"/>
		<updated>2014-11-24T11:48:17Z</updated>

		<summary type="html">&lt;p&gt;&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;Vlastnosti&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;cs&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;← Starší verze&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;Verze z 24. 11. 2014, 11:48&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l41&quot; &gt;Řádek 41:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Řádek 41:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;*Je-li &amp;lt;math&amp;gt;T&amp;lt;/math&amp;gt; '''sporná''', potom &amp;lt;math&amp;gt;\forall \varphi,\psi \in \mathit{Form_L} : T\vdash \varphi\leftrightarrow\psi&amp;lt;/math&amp;gt; a tedy &amp;lt;math&amp;gt;|B(T)|=1&amp;lt;/math&amp;gt; a tedy i &amp;lt;math&amp;gt;|L(T)|=1&amp;lt;/math&amp;gt;.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;*Je-li &amp;lt;math&amp;gt;T&amp;lt;/math&amp;gt; '''sporná''', potom &amp;lt;math&amp;gt;\forall \varphi,\psi \in \mathit{Form_L} : T\vdash \varphi\leftrightarrow\psi&amp;lt;/math&amp;gt; a tedy &amp;lt;math&amp;gt;|B(T)|=1&amp;lt;/math&amp;gt; a tedy i &amp;lt;math&amp;gt;|L(T)|=1&amp;lt;/math&amp;gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;*Je-li &amp;lt;math&amp;gt;T&amp;lt;/math&amp;gt; '''bezesporná''', je &amp;lt;math&amp;gt;|B(T)|\geq2&amp;lt;/math&amp;gt; neboť &amp;lt;math&amp;gt;T \vdash  \neg(\varphi \vee \neg\varphi \leftrightarrow \varphi \&amp;amp; \neg\varphi)&amp;lt;/math&amp;gt; a proto &amp;lt;math&amp;gt;[\varphi \vee \neg\varphi]_{\equiv_T}~\neq~[\varphi \&amp;amp; \neg\varphi]_{\equiv_T}&amp;lt;/math&amp;gt;.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;*Je-li &amp;lt;math&amp;gt;T&amp;lt;/math&amp;gt; '''bezesporná''', je &amp;lt;math&amp;gt;|B(T)|\geq2&amp;lt;/math&amp;gt; neboť &amp;lt;math&amp;gt;T \vdash  \neg(\varphi \vee \neg\varphi \leftrightarrow \varphi \&amp;amp; \neg\varphi)&amp;lt;/math&amp;gt; a proto &amp;lt;math&amp;gt;[\varphi \vee \neg\varphi]_{\equiv_T}~\neq~[\varphi \&amp;amp; \neg\varphi]_{\equiv_T}&amp;lt;/math&amp;gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;*Je-li &amp;lt;math&amp;gt;T&amp;lt;/math&amp;gt; '''bezesporná''' a navíc '''úplná''' dostáváme &amp;lt;math&amp;gt;|L(T)|=2&amp;lt;/math&amp;gt; neboť z úplnosti &amp;lt;math&amp;gt;T&amp;lt;/math&amp;gt; plyne, že &amp;lt;math&amp;gt;\forall \sigma \in \mathit{Sent_L} : T \vdash \sigma nebo T \vdash \neg\sigma&amp;lt;/math&amp;gt; a tedy &amp;lt;math&amp;gt;T \vdash \sigma \leftrightarrow \top&amp;lt;/math&amp;gt; nebo &amp;lt;math&amp;gt;T \vdash \sigma \leftrightarrow \bot&amp;lt;/math&amp;gt; z čehož plyne, že &amp;lt;math&amp;gt;[\sigma]_{\equiv_T} \in [\varphi \vee \neg\varphi]_{\equiv_T}&amp;lt;/math&amp;gt; nebo &amp;lt;math&amp;gt;[\sigma]_{\equiv_T} \in [\varphi \&amp;amp; \neg\varphi]_{\equiv_T}&amp;lt;/math&amp;gt; a tedy &amp;lt;math&amp;gt;L(T)=\{[\varphi \vee \neg\varphi]_{\equiv_T},[\varphi \&amp;amp; \neg\varphi]_{\equiv_T}\}&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;*Je-li &amp;lt;math&amp;gt;T&amp;lt;/math&amp;gt; '''bezesporná''' a navíc '''úplná''' dostáváme &amp;lt;math&amp;gt;|L(T)|=2&amp;lt;/math&amp;gt; neboť z úplnosti &amp;lt;math&amp;gt;T&amp;lt;/math&amp;gt; plyne, že &amp;lt;math&amp;gt;\forall \sigma \in \mathit{Sent_L} : T \vdash \sigma&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;lt;/math&amp;gt; &lt;/ins&gt;nebo &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;lt;math&amp;gt;&lt;/ins&gt;T \vdash \neg\sigma&amp;lt;/math&amp;gt; a tedy &amp;lt;math&amp;gt;T \vdash \sigma \leftrightarrow \top&amp;lt;/math&amp;gt; nebo &amp;lt;math&amp;gt;T \vdash \sigma \leftrightarrow \bot&amp;lt;/math&amp;gt; z čehož plyne, že &amp;lt;math&amp;gt;[\sigma]_{\equiv_T} \in [\varphi \vee \neg\varphi]_{\equiv_T}&amp;lt;/math&amp;gt; nebo &amp;lt;math&amp;gt;[\sigma]_{\equiv_T} \in [\varphi \&amp;amp; \neg\varphi]_{\equiv_T}&amp;lt;/math&amp;gt; a tedy &amp;lt;math&amp;gt;L(T)=\{[\varphi \vee \neg\varphi]_{\equiv_T},[\varphi \&amp;amp; \neg\varphi]_{\equiv_T}\}&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;*Je-li &amp;lt;math&amp;gt;T&amp;lt;/math&amp;gt; '''bezesporná''' a '''neúplná''' potom &amp;lt;math&amp;gt;|L(T)|\geq 4&amp;lt;/math&amp;gt; neboť existuje sentence &amp;lt;math&amp;gt;\sigma&amp;lt;/math&amp;gt; t.ž. &amp;lt;math&amp;gt;T \nvdash \sigma&amp;lt;/math&amp;gt; a &amp;lt;math&amp;gt;T \nvdash\neg\sigma&amp;lt;/math&amp;gt; a tudíž &amp;lt;math&amp;gt;\sigma \notin [\top]_{\equiv_T}&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;\sigma \notin [\bot]_{\equiv_T}&amp;lt;/math&amp;gt; a proto jsou &amp;lt;math&amp;gt;[\top]_{\equiv_T},[\bot]_{\equiv_T},[\sigma]_{\equiv_T},[\neg\sigma]_{\equiv_T}&amp;lt;/math&amp;gt; čtyři navzájem různé prvky &amp;lt;math&amp;gt;L(T)&amp;lt;/math&amp;gt;.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;*Je-li &amp;lt;math&amp;gt;T&amp;lt;/math&amp;gt; '''bezesporná''' a '''neúplná''' potom &amp;lt;math&amp;gt;|L(T)|\geq 4&amp;lt;/math&amp;gt; neboť existuje sentence &amp;lt;math&amp;gt;\sigma&amp;lt;/math&amp;gt; t.ž. &amp;lt;math&amp;gt;T \nvdash \sigma&amp;lt;/math&amp;gt; a &amp;lt;math&amp;gt;T \nvdash\neg\sigma&amp;lt;/math&amp;gt; a tudíž &amp;lt;math&amp;gt;\sigma \notin [\top]_{\equiv_T}&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;\sigma \notin [\bot]_{\equiv_T}&amp;lt;/math&amp;gt; a proto jsou &amp;lt;math&amp;gt;[\top]_{\equiv_T},[\bot]_{\equiv_T},[\sigma]_{\equiv_T},[\neg\sigma]_{\equiv_T}&amp;lt;/math&amp;gt; čtyři navzájem různé prvky &amp;lt;math&amp;gt;L(T)&amp;lt;/math&amp;gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;*Každá Booleova algebra je izomorfní Lindenbaum-Tarského algebře &amp;lt;math&amp;gt;LT(T)&amp;lt;/math&amp;gt; pro vhodné &amp;lt;math&amp;gt;T&amp;lt;/math&amp;gt;.&amp;lt;ref&amp;gt;Handbook of Boolean Algebras: Volume 1, North-Holland 1989, Theorem 9.10&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;*Každá Booleova algebra je izomorfní Lindenbaum-Tarského algebře &amp;lt;math&amp;gt;LT(T)&amp;lt;/math&amp;gt; pro vhodné &amp;lt;math&amp;gt;T&amp;lt;/math&amp;gt;.&amp;lt;ref&amp;gt;Handbook of Boolean Algebras: Volume 1, North-Holland 1989, Theorem 9.10&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>HonzaB</name></author>
		
	</entry>
	<entry>
		<id>https://wikisofia.cz/w/index.php?title=Lindenbaum-Tarsk%C3%A9ho_algebry&amp;diff=9444&amp;oldid=prev</id>
		<title>HonzaB: /* Konstrukce */</title>
		<link rel="alternate" type="text/html" href="https://wikisofia.cz/w/index.php?title=Lindenbaum-Tarsk%C3%A9ho_algebry&amp;diff=9444&amp;oldid=prev"/>
		<updated>2014-11-24T11:46:59Z</updated>

		<summary type="html">&lt;p&gt;&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;Konstrukce&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;cs&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;← Starší verze&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;Verze z 24. 11. 2014, 11:46&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l8&quot; &gt;Řádek 8:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Řádek 8:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Označme nyní &amp;lt;math&amp;gt;[\varphi]_{\equiv_T}&amp;lt;/math&amp;gt; ekvivalenční třídu pro &amp;lt;math&amp;gt;\varphi&amp;lt;/math&amp;gt; a uvažme &amp;lt;math&amp;gt;B(T)=\{[\varphi]_{\equiv_T}| \varphi \in \mathit{Form_L}\}&amp;lt;/math&amp;gt;  na níž definujme operace &amp;lt;math&amp;gt;\wedge&amp;lt;/math&amp;gt; ('''průsek'''), &amp;lt;math&amp;gt;\vee&amp;lt;/math&amp;gt; ('''sjednocení'''), &amp;lt;math&amp;gt;-&amp;lt;/math&amp;gt; ('''komplement''') a prvky &amp;lt;math&amp;gt;\textbf{1}&amp;lt;/math&amp;gt; ('''maximální prvek'''), &amp;lt;math&amp;gt;\textbf{0}&amp;lt;/math&amp;gt; ('''minimální prvek''') takto:&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Označme nyní &amp;lt;math&amp;gt;[\varphi]_{\equiv_T}&amp;lt;/math&amp;gt; ekvivalenční třídu pro &amp;lt;math&amp;gt;\varphi&amp;lt;/math&amp;gt; a uvažme &amp;lt;math&amp;gt;B(T)=\{[\varphi]_{\equiv_T}| \varphi \in \mathit{Form_L}\}&amp;lt;/math&amp;gt;  na níž definujme operace &amp;lt;math&amp;gt;\wedge&amp;lt;/math&amp;gt; ('''průsek'''), &amp;lt;math&amp;gt;\vee&amp;lt;/math&amp;gt; ('''sjednocení'''), &amp;lt;math&amp;gt;-&amp;lt;/math&amp;gt; ('''komplement''') a prvky &amp;lt;math&amp;gt;\textbf{1}&amp;lt;/math&amp;gt; ('''maximální prvek'''), &amp;lt;math&amp;gt;\textbf{0}&amp;lt;/math&amp;gt; ('''minimální prvek''') takto:&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;math&amp;gt;[\varphi]_{\equiv_T} \wedge [\psi]_{\equiv_T} &amp;amp;= [\varphi \&amp;amp; \psi]_{\equiv_T}&amp;lt;/math&amp;gt;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot;&gt; &lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;math&amp;gt;[\varphi]_{\equiv_T} \vee [\psi]_{\equiv_T} &amp;amp;= [\varphi \vee \psi]_{\equiv_T}&amp;lt;/math&amp;gt;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot;&gt; &lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt; &lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[\varphi]_{\equiv_T} \wedge [\psi]_{\equiv_T} &amp;amp;= [\varphi \&amp;amp; \psi]_{\equiv_T}&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt; &lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[\varphi]_{\equiv_T} \vee [\psi]_{\equiv_T} &amp;amp;= [\varphi \vee \psi]_{\equiv_T}&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;-[\varphi]_{\equiv_T} &amp;amp;= [\neg\varphi]&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;-[\varphi]_{\equiv_T} &amp;amp;= [\neg\varphi]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;\textbf{1} &amp;amp;= [\varphi \vee \neg\varphi]_{\equiv_T}&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;\textbf{1} &amp;amp;= [\varphi \vee \neg\varphi]_{\equiv_T}&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>HonzaB</name></author>
		
	</entry>
	<entry>
		<id>https://wikisofia.cz/w/index.php?title=Lindenbaum-Tarsk%C3%A9ho_algebry&amp;diff=9443&amp;oldid=prev</id>
		<title>HonzaB: /* Konstrukce */</title>
		<link rel="alternate" type="text/html" href="https://wikisofia.cz/w/index.php?title=Lindenbaum-Tarsk%C3%A9ho_algebry&amp;diff=9443&amp;oldid=prev"/>
		<updated>2014-11-24T11:45:44Z</updated>

		<summary type="html">&lt;p&gt;&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;Konstrukce&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;cs&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;← Starší verze&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;Verze z 24. 11. 2014, 11:45&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l8&quot; &gt;Řádek 8:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Řádek 8:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Označme nyní &amp;lt;math&amp;gt;[\varphi]_{\equiv_T}&amp;lt;/math&amp;gt; ekvivalenční třídu pro &amp;lt;math&amp;gt;\varphi&amp;lt;/math&amp;gt; a uvažme &amp;lt;math&amp;gt;B(T)=\{[\varphi]_{\equiv_T}| \varphi \in \mathit{Form_L}\}&amp;lt;/math&amp;gt;  na níž definujme operace &amp;lt;math&amp;gt;\wedge&amp;lt;/math&amp;gt; ('''průsek'''), &amp;lt;math&amp;gt;\vee&amp;lt;/math&amp;gt; ('''sjednocení'''), &amp;lt;math&amp;gt;-&amp;lt;/math&amp;gt; ('''komplement''') a prvky &amp;lt;math&amp;gt;\textbf{1}&amp;lt;/math&amp;gt; ('''maximální prvek'''), &amp;lt;math&amp;gt;\textbf{0}&amp;lt;/math&amp;gt; ('''minimální prvek''') takto:&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Označme nyní &amp;lt;math&amp;gt;[\varphi]_{\equiv_T}&amp;lt;/math&amp;gt; ekvivalenční třídu pro &amp;lt;math&amp;gt;\varphi&amp;lt;/math&amp;gt; a uvažme &amp;lt;math&amp;gt;B(T)=\{[\varphi]_{\equiv_T}| \varphi \in \mathit{Form_L}\}&amp;lt;/math&amp;gt;  na níž definujme operace &amp;lt;math&amp;gt;\wedge&amp;lt;/math&amp;gt; ('''průsek'''), &amp;lt;math&amp;gt;\vee&amp;lt;/math&amp;gt; ('''sjednocení'''), &amp;lt;math&amp;gt;-&amp;lt;/math&amp;gt; ('''komplement''') a prvky &amp;lt;math&amp;gt;\textbf{1}&amp;lt;/math&amp;gt; ('''maximální prvek'''), &amp;lt;math&amp;gt;\textbf{0}&amp;lt;/math&amp;gt; ('''minimální prvek''') takto:&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;math&amp;gt;[\varphi]_{\equiv_T} \wedge [\psi]_{\equiv_T} &amp;amp;= [\varphi \&amp;amp; \psi]_{\equiv_T}&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;\t&lt;/del&gt;[\varphi]_{\equiv_T} \wedge [\psi]_{\equiv_T} &amp;amp;= [\varphi \&amp;amp; \psi]_{\equiv_T}&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot;&gt; &lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;math&amp;gt;[\varphi]_{\equiv_T} \vee [\psi]_{\equiv_T} &amp;amp;= [\varphi \vee \psi]_{\equiv_T}&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;math&amp;gt;[\varphi]_{\equiv_T} \vee [\psi]_{\equiv_T} &amp;amp;= [\varphi \vee \psi]_{\equiv_T}&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>HonzaB</name></author>
		
	</entry>
	<entry>
		<id>https://wikisofia.cz/w/index.php?title=Lindenbaum-Tarsk%C3%A9ho_algebry&amp;diff=9442&amp;oldid=prev</id>
		<title>HonzaB: /* Konstrukce */</title>
		<link rel="alternate" type="text/html" href="https://wikisofia.cz/w/index.php?title=Lindenbaum-Tarsk%C3%A9ho_algebry&amp;diff=9442&amp;oldid=prev"/>
		<updated>2014-11-24T11:44:54Z</updated>

		<summary type="html">&lt;p&gt;&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;Konstrukce&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;cs&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;← Starší verze&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;Verze z 24. 11. 2014, 11:44&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l9&quot; &gt;Řádek 9:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Řádek 9:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;begin{align*}&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;\t&lt;/ins&gt;[\varphi]_{\equiv_T} \wedge [\psi]_{\equiv_T} &amp;amp;= [\varphi \&amp;amp; \psi]_{\equiv_T}&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;lt;/math&amp;gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[\varphi]_{\equiv_T} \wedge [\psi]_{\equiv_T} &amp;amp;= [\varphi \&amp;amp; \psi]_{\equiv_T}&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;lt;math&amp;gt;[&lt;/ins&gt;\varphi]_{\equiv_T} \vee [\psi]_{\equiv_T} &amp;amp;= [\varphi \vee \psi]_{\equiv_T}&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;lt;/math&amp;gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;\varphi]_{\equiv_T} \vee [\psi]_{\equiv_T} &amp;amp;= [\varphi \vee \psi]_{\equiv_T}&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;lt;math&amp;gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;-[\varphi]_{\equiv_T} &amp;amp;= [\neg\varphi]&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;-[\varphi]_{\equiv_T} &amp;amp;= [\neg\varphi]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;\textbf{1} &amp;amp;= [\varphi \vee \neg\varphi]_{\equiv_T}&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;\textbf{1} &amp;amp;= [\varphi \vee \neg\varphi]_{\equiv_T}&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;\textbf{0} &amp;amp;= [\varphi \&amp;amp; \neg\varphi]_{\equiv_T}&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;\textbf{0} &amp;amp;= [\varphi \&amp;amp; \neg\varphi]_{\equiv_T}&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;end{align*}&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot;&gt; &lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>HonzaB</name></author>
		
	</entry>
	<entry>
		<id>https://wikisofia.cz/w/index.php?title=Lindenbaum-Tarsk%C3%A9ho_algebry&amp;diff=9441&amp;oldid=prev</id>
		<title>HonzaB: /* Konstrukce */</title>
		<link rel="alternate" type="text/html" href="https://wikisofia.cz/w/index.php?title=Lindenbaum-Tarsk%C3%A9ho_algebry&amp;diff=9441&amp;oldid=prev"/>
		<updated>2014-11-24T11:42:20Z</updated>

		<summary type="html">&lt;p&gt;&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;Konstrukce&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;cs&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;← Starší verze&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;Verze z 24. 11. 2014, 11:42&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l9&quot; &gt;Řádek 9:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Řádek 9:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;\&lt;/del&gt;begin{align*}&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;begin{align*}&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[\varphi]_{\equiv_T} \wedge [\psi]_{\equiv_T} &amp;amp;= [\varphi \&amp;amp; \psi]_{\equiv_T}&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[\varphi]_{\equiv_T} \wedge [\psi]_{\equiv_T} &amp;amp;= [\varphi \&amp;amp; \psi]_{\equiv_T}&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;\varphi]_{\equiv_T} \vee [\psi]_{\equiv_T} &amp;amp;= [\varphi \vee \psi]_{\equiv_T}&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;\varphi]_{\equiv_T} \vee [\psi]_{\equiv_T} &amp;amp;= [\varphi \vee \psi]_{\equiv_T}&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l15&quot; &gt;Řádek 15:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Řádek 15:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;\textbf{1} &amp;amp;= [\varphi \vee \neg\varphi]_{\equiv_T}&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;\textbf{1} &amp;amp;= [\varphi \vee \neg\varphi]_{\equiv_T}&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;\textbf{0} &amp;amp;= [\varphi \&amp;amp; \neg\varphi]_{\equiv_T}&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;\textbf{0} &amp;amp;= [\varphi \&amp;amp; \neg\varphi]_{\equiv_T}&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;\&lt;/del&gt;end{align*}&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;end{align*}&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l37&quot; &gt;Řádek 37:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Řádek 37:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Stojí za povšimnutí, že uspořádání na &amp;lt;math&amp;gt;\mathbb{B}(T)&amp;lt;/math&amp;gt; lze interpretovat jako ''&amp;quot;čím blíže je &amp;lt;math&amp;gt;[\varphi]&amp;lt;/math&amp;gt; k &amp;lt;math&amp;gt;\textbf{0}&amp;lt;/math&amp;gt; tím silnějším je tvrzením&amp;quot;'' (blízkost nule může odpovídat snadnosti falsifikace, &amp;lt;math&amp;gt;\textbf{0}&amp;lt;/math&amp;gt; je falsisikovaná vždy naopak &amp;lt;math&amp;gt;\textbf{1}&amp;lt;/math&amp;gt; není falsifikovatelná nikdy). Mimo jiné tato interpretace plyne i z triviálního faktu, že čím blíže je &amp;lt;math&amp;gt;[\varphi]&amp;lt;/math&amp;gt; k &amp;lt;math&amp;gt;\textbf{0}&amp;lt;/math&amp;gt; tím větší (co do inkluze) je množina následníků tj. čím silnější předpoklad učiníme, tím více závěrů jsme schopni udělat. S touto interpretací se můžeme setkat například ve [[Forcing|forcingu]], kde &amp;lt;math&amp;gt;p\leq q&amp;lt;/math&amp;gt; interpretujeme jako ''&amp;quot;&amp;lt;math&amp;gt;p&amp;lt;/math&amp;gt; je silnější podmínka než &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt;&amp;quot;''.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Stojí za povšimnutí, že uspořádání na &amp;lt;math&amp;gt;\mathbb{B}(T)&amp;lt;/math&amp;gt; lze interpretovat jako ''&amp;quot;čím blíže je &amp;lt;math&amp;gt;[\varphi]&amp;lt;/math&amp;gt; k &amp;lt;math&amp;gt;\textbf{0}&amp;lt;/math&amp;gt; tím silnějším je tvrzením&amp;quot;'' (blízkost nule může odpovídat snadnosti falsifikace, &amp;lt;math&amp;gt;\textbf{0}&amp;lt;/math&amp;gt; je falsisikovaná vždy naopak &amp;lt;math&amp;gt;\textbf{1}&amp;lt;/math&amp;gt; není falsifikovatelná nikdy). Mimo jiné tato interpretace plyne i z triviálního faktu, že čím blíže je &amp;lt;math&amp;gt;[\varphi]&amp;lt;/math&amp;gt; k &amp;lt;math&amp;gt;\textbf{0}&amp;lt;/math&amp;gt; tím větší (co do inkluze) je množina následníků tj. čím silnější předpoklad učiníme, tím více závěrů jsme schopni udělat. S touto interpretací se můžeme setkat například ve [[Forcing|forcingu]], kde &amp;lt;math&amp;gt;p\leq q&amp;lt;/math&amp;gt; interpretujeme jako ''&amp;quot;&amp;lt;math&amp;gt;p&amp;lt;/math&amp;gt; je silnější podmínka než &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt;&amp;quot;''.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt; &lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Definice ==&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Definice ==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Nechť &amp;lt;math&amp;gt;T&amp;lt;/math&amp;gt; je teorie prvořádové predikátové logiky a &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; její jazyk, potom &amp;lt;math&amp;gt;\mathbb{LT}(T)=&amp;lt;LT(T),\wedge,\vee,-,\textbf{0},\textbf{1}&amp;gt;&amp;lt;/math&amp;gt; kde  &amp;lt;math&amp;gt;LT(T)=\{[\varphi]_{\equiv_T}| \varphi \in \mathit{Sent_L}\}&amp;lt;/math&amp;gt; a  &amp;lt;math&amp;gt;\equiv_T&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;\wedge&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;\vee&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;-&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;\textbf{0}&amp;lt;/math&amp;gt; a &amp;lt;math&amp;gt;\textbf{1}&amp;lt;/math&amp;gt; jsou definovány jako v ''Konstrukci'' výše, nazveme '''Lindenbaum-Tarského algebrou pro teorii''' &amp;lt;math&amp;gt;T&amp;lt;/math&amp;gt;.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Nechť &amp;lt;math&amp;gt;T&amp;lt;/math&amp;gt; je teorie prvořádové predikátové logiky a &amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; její jazyk, potom &amp;lt;math&amp;gt;\mathbb{LT}(T)=&amp;lt;LT(T),\wedge,\vee,-,\textbf{0},\textbf{1}&amp;gt;&amp;lt;/math&amp;gt; kde  &amp;lt;math&amp;gt;LT(T)=\{[\varphi]_{\equiv_T}| \varphi \in \mathit{Sent_L}\}&amp;lt;/math&amp;gt; a  &amp;lt;math&amp;gt;\equiv_T&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;\wedge&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;\vee&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;-&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;\textbf{0}&amp;lt;/math&amp;gt; a &amp;lt;math&amp;gt;\textbf{1}&amp;lt;/math&amp;gt; jsou definovány jako v ''Konstrukci'' výše, nazveme '''Lindenbaum-Tarského algebrou pro teorii''' &amp;lt;math&amp;gt;T&amp;lt;/math&amp;gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>HonzaB</name></author>
		
	</entry>
	<entry>
		<id>https://wikisofia.cz/w/index.php?title=Lindenbaum-Tarsk%C3%A9ho_algebry&amp;diff=9439&amp;oldid=prev</id>
		<title>HonzaB: /* Vlastnosti */</title>
		<link rel="alternate" type="text/html" href="https://wikisofia.cz/w/index.php?title=Lindenbaum-Tarsk%C3%A9ho_algebry&amp;diff=9439&amp;oldid=prev"/>
		<updated>2014-11-24T11:41:10Z</updated>

		<summary type="html">&lt;p&gt;&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;Vlastnosti&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;cs&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;← Starší verze&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;Verze z 24. 11. 2014, 11:41&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l41&quot; &gt;Řádek 41:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Řádek 41:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Vlastnosti ==&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Vlastnosti ==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;*Je-li &amp;lt;math&amp;gt;T&amp;lt;/math&amp;gt; '''sporná''', potom &amp;lt;math&amp;gt;\forall \varphi,\psi \in \mathit{Form_L} : T\vdash \varphi\leftrightarrow\psi&amp;lt;/math&amp;gt; a tedy &amp;lt;math&amp;gt;|B(T)|=1&amp;lt;/math&amp;gt; a tedy i &amp;lt;math&amp;gt;|L(T)|=1&amp;lt;/math&amp;gt;.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;*Je-li &amp;lt;math&amp;gt;T&amp;lt;/math&amp;gt; '''sporná''', potom &amp;lt;math&amp;gt;\forall \varphi,\psi \in \mathit{Form_L} : T\vdash \varphi\leftrightarrow\psi&amp;lt;/math&amp;gt; a tedy &amp;lt;math&amp;gt;|B(T)|=1&amp;lt;/math&amp;gt; a tedy i &amp;lt;math&amp;gt;|L(T)|=1&amp;lt;/math&amp;gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;*Je-li &amp;lt;math&amp;gt;T&amp;lt;/math&amp;gt; '''bezesporná''', je &amp;lt;math&amp;gt;|B(T)|\geq2&amp;lt;math&amp;gt; neboť &amp;lt;math&amp;gt;T \vdash  \neg(\varphi \vee \neg\varphi \leftrightarrow \varphi \&amp;amp; \neg\varphi)&amp;lt;/math&amp;gt; a proto &amp;lt;math&amp;gt;[\varphi \vee \neg\varphi]_{\equiv_T}~\neq~[\varphi \&amp;amp; \neg\varphi]_{\equiv_T}&amp;lt;/math&amp;gt;.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;*Je-li &amp;lt;math&amp;gt;T&amp;lt;/math&amp;gt; '''bezesporná''', je &amp;lt;math&amp;gt;|B(T)|\geq2&amp;lt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;/&lt;/ins&gt;math&amp;gt; neboť &amp;lt;math&amp;gt;T \vdash  \neg(\varphi \vee \neg\varphi \leftrightarrow \varphi \&amp;amp; \neg\varphi)&amp;lt;/math&amp;gt; a proto &amp;lt;math&amp;gt;[\varphi \vee \neg\varphi]_{\equiv_T}~\neq~[\varphi \&amp;amp; \neg\varphi]_{\equiv_T}&amp;lt;/math&amp;gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;*Je-li &amp;lt;math&amp;gt;T&amp;lt;/math&amp;gt; '''bezesporná''' a navíc '''úplná''' dostáváme &amp;lt;math&amp;gt;|L(T)|=2&amp;lt;/math&amp;gt; neboť z úplnosti &amp;lt;math&amp;gt;T&amp;lt;/math&amp;gt; plyne, že &amp;lt;math&amp;gt;\forall \sigma \in \mathit{Sent_L} : T \vdash \sigma nebo T \vdash \neg\sigma&amp;lt;/math&amp;gt; a tedy &amp;lt;math&amp;gt;T \vdash \sigma \leftrightarrow \top&amp;lt;/math&amp;gt; nebo &amp;lt;math&amp;gt;T \vdash \sigma \leftrightarrow \bot&amp;lt;/math&amp;gt; z čehož plyne, že &amp;lt;math&amp;gt;[\sigma]_{\equiv_T} \in [\varphi \vee \neg\varphi]_{\equiv_T}&amp;lt;/math&amp;gt; nebo &amp;lt;math&amp;gt;[\sigma]_{\equiv_T} \in [\varphi \&amp;amp; \neg\varphi]_{\equiv_T}&amp;lt;/math&amp;gt; a tedy &amp;lt;math&amp;gt;L(T)=\{[\varphi \vee \neg\varphi]_{\equiv_T},[\varphi \&amp;amp; \neg\varphi]_{\equiv_T}\}&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;*Je-li &amp;lt;math&amp;gt;T&amp;lt;/math&amp;gt; '''bezesporná''' a navíc '''úplná''' dostáváme &amp;lt;math&amp;gt;|L(T)|=2&amp;lt;/math&amp;gt; neboť z úplnosti &amp;lt;math&amp;gt;T&amp;lt;/math&amp;gt; plyne, že &amp;lt;math&amp;gt;\forall \sigma \in \mathit{Sent_L} : T \vdash \sigma nebo T \vdash \neg\sigma&amp;lt;/math&amp;gt; a tedy &amp;lt;math&amp;gt;T \vdash \sigma \leftrightarrow \top&amp;lt;/math&amp;gt; nebo &amp;lt;math&amp;gt;T \vdash \sigma \leftrightarrow \bot&amp;lt;/math&amp;gt; z čehož plyne, že &amp;lt;math&amp;gt;[\sigma]_{\equiv_T} \in [\varphi \vee \neg\varphi]_{\equiv_T}&amp;lt;/math&amp;gt; nebo &amp;lt;math&amp;gt;[\sigma]_{\equiv_T} \in [\varphi \&amp;amp; \neg\varphi]_{\equiv_T}&amp;lt;/math&amp;gt; a tedy &amp;lt;math&amp;gt;L(T)=\{[\varphi \vee \neg\varphi]_{\equiv_T},[\varphi \&amp;amp; \neg\varphi]_{\equiv_T}\}&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;*Je-li &amp;lt;math&amp;gt;T&amp;lt;/math&amp;gt; '''bezesporná''' a '''neúplná''' potom &amp;lt;math&amp;gt;|L(T)|\geq 4&amp;lt;/math&amp;gt; neboť existuje sentence &amp;lt;math&amp;gt;\sigma&amp;lt;/math&amp;gt; t.ž. &amp;lt;math&amp;gt;T \nvdash \sigma&amp;lt;/math&amp;gt; a &amp;lt;math&amp;gt;T \nvdash\neg\sigma&amp;lt;/math&amp;gt; a tudíž &amp;lt;math&amp;gt;\sigma \notin [\top]_{\equiv_T}&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;\sigma \notin [\bot]_{\equiv_T}&amp;lt;/math&amp;gt; a proto jsou &amp;lt;math&amp;gt;[\top]_{\equiv_T},[\bot]_{\equiv_T},[\sigma]_{\equiv_T},[\neg\sigma]_{\equiv_T}&amp;lt;/math&amp;gt; čtyři navzájem různé prvky &amp;lt;math&amp;gt;L(T)&amp;lt;/math&amp;gt;.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;*Je-li &amp;lt;math&amp;gt;T&amp;lt;/math&amp;gt; '''bezesporná''' a '''neúplná''' potom &amp;lt;math&amp;gt;|L(T)|\geq 4&amp;lt;/math&amp;gt; neboť existuje sentence &amp;lt;math&amp;gt;\sigma&amp;lt;/math&amp;gt; t.ž. &amp;lt;math&amp;gt;T \nvdash \sigma&amp;lt;/math&amp;gt; a &amp;lt;math&amp;gt;T \nvdash\neg\sigma&amp;lt;/math&amp;gt; a tudíž &amp;lt;math&amp;gt;\sigma \notin [\top]_{\equiv_T}&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;\sigma \notin [\bot]_{\equiv_T}&amp;lt;/math&amp;gt; a proto jsou &amp;lt;math&amp;gt;[\top]_{\equiv_T},[\bot]_{\equiv_T},[\sigma]_{\equiv_T},[\neg\sigma]_{\equiv_T}&amp;lt;/math&amp;gt; čtyři navzájem různé prvky &amp;lt;math&amp;gt;L(T)&amp;lt;/math&amp;gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>HonzaB</name></author>
		
	</entry>
	<entry>
		<id>https://wikisofia.cz/w/index.php?title=Lindenbaum-Tarsk%C3%A9ho_algebry&amp;diff=9438&amp;oldid=prev</id>
		<title>HonzaB: /* \mathcal{L}_n(P,\mathfrak{A}) */</title>
		<link rel="alternate" type="text/html" href="https://wikisofia.cz/w/index.php?title=Lindenbaum-Tarsk%C3%A9ho_algebry&amp;diff=9438&amp;oldid=prev"/>
		<updated>2014-11-24T11:39:42Z</updated>

		<summary type="html">&lt;p&gt;&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;\mathcal{L}_n(P,\mathfrak{A})&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;cs&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;← Starší verze&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;Verze z 24. 11. 2014, 11:39&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l49&quot; &gt;Řádek 49:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Řádek 49:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{| class=&amp;quot;wikitable&amp;quot;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{| class=&amp;quot;wikitable&amp;quot;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|-&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|-&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| '''Definice:''' Nechť &amp;lt;math&amp;gt;\mathfrak{A}&amp;lt;/math&amp;gt; je struktura s nosičem &amp;lt;math&amp;gt;A&amp;lt;/math&amp;gt; a &amp;lt;math&amp;gt;P\subseteq A&amp;lt;/math&amp;gt;, potom &amp;lt;math&amp;gt;\mathcal{L}(P)&amp;lt;/math&amp;gt; je jazyk obsahující pouze parametry z &amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; a &amp;lt;math&amp;gt;\mathit{Form^n_{\mathcal{L}(P)}}&amp;lt;/math&amp;gt; množina formulí &amp;lt;math&amp;gt;\varphi&amp;lt;/math&amp;gt; v jazyce &amp;lt;math&amp;gt;\mathcal{L}(P)&amp;lt;/math&amp;gt; kde &amp;lt;math&amp;gt;\varphi&amp;lt;/math&amp;gt; má právě &amp;lt;math&amp;gt;n&amp;lt;/math&amp;gt;volných proměnných.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| '''Definice:''' Nechť &amp;lt;math&amp;gt;\mathfrak{A}&amp;lt;/math&amp;gt; je struktura s nosičem &amp;lt;math&amp;gt;A&amp;lt;/math&amp;gt; a &amp;lt;math&amp;gt;P\subseteq A&amp;lt;/math&amp;gt;, potom &amp;lt;math&amp;gt;\mathcal{L}(P)&amp;lt;/math&amp;gt; je jazyk obsahující pouze parametry z &amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; a &amp;lt;math&amp;gt;\mathit{Form^n_{\mathcal{L}(P)}}&amp;lt;/math&amp;gt; množina formulí &amp;lt;math&amp;gt;\varphi&amp;lt;/math&amp;gt; v jazyce &amp;lt;math&amp;gt;\mathcal{L}(P)&amp;lt;/math&amp;gt; kde &amp;lt;math&amp;gt;\varphi&amp;lt;/math&amp;gt; má právě &amp;lt;math&amp;gt;n&amp;lt;/math&amp;gt; volných proměnných.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|}&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|}&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Na množině &amp;lt;math&amp;gt;\mathit{Form^n_{\mathcal{L}(P)}}&amp;lt;/math&amp;gt; můžeme opět zavést ekvivalenci &amp;lt;math&amp;gt;\equiv_T&amp;lt;/math&amp;gt; jako výše v ''Konstrukci''. Zadefinujeme-li také &amp;lt;math&amp;gt;\equiv_T&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;\wedge&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;\vee&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;-&amp;lt;/math&amp;gt;,&amp;lt;math&amp;gt;\textbf{0}&amp;lt;/math&amp;gt; a &amp;lt;math&amp;gt;\textbf{1}&amp;lt;/math&amp;gt; jako v ''Konstrukci'' výše a zvolíme &amp;lt;math&amp;gt;T=Th(\mathfrak{A})&amp;lt;/math&amp;gt; získáme [[Booleova algebra|Booleovu algebru]], jež značíme &amp;lt;math&amp;gt;\mathcal{L}_n(P,\mathfrak{A})&amp;lt;/math&amp;gt;.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Na množině &amp;lt;math&amp;gt;\mathit{Form^n_{\mathcal{L}(P)}}&amp;lt;/math&amp;gt; můžeme opět zavést ekvivalenci &amp;lt;math&amp;gt;\equiv_T&amp;lt;/math&amp;gt; jako výše v ''Konstrukci''. Zadefinujeme-li také &amp;lt;math&amp;gt;\equiv_T&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;\wedge&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;\vee&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;-&amp;lt;/math&amp;gt;,&amp;lt;math&amp;gt;\textbf{0}&amp;lt;/math&amp;gt; a &amp;lt;math&amp;gt;\textbf{1}&amp;lt;/math&amp;gt; jako v ''Konstrukci'' výše a zvolíme &amp;lt;math&amp;gt;T=Th(\mathfrak{A})&amp;lt;/math&amp;gt; získáme [[Booleova algebra|Booleovu algebru]], jež značíme &amp;lt;math&amp;gt;\mathcal{L}_n(P,\mathfrak{A})&amp;lt;/math&amp;gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>HonzaB</name></author>
		
	</entry>
	<entry>
		<id>https://wikisofia.cz/w/index.php?title=Lindenbaum-Tarsk%C3%A9ho_algebry&amp;diff=9437&amp;oldid=prev</id>
		<title>HonzaB: /* ﻿$ \mathcal{L}_n(P,\mathfrak{A}) $
﻿ */</title>
		<link rel="alternate" type="text/html" href="https://wikisofia.cz/w/index.php?title=Lindenbaum-Tarsk%C3%A9ho_algebry&amp;diff=9437&amp;oldid=prev"/>
		<updated>2014-11-24T11:38:52Z</updated>

		<summary type="html">&lt;p&gt;&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;﻿$ \mathcal{L}_n(P,\mathfrak{A}) $ ﻿&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;cs&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;← Starší verze&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;Verze z 24. 11. 2014, 11:38&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l49&quot; &gt;Řádek 49:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Řádek 49:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{| class=&amp;quot;wikitable&amp;quot;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{| class=&amp;quot;wikitable&amp;quot;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|-&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|-&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| '''Definice:''' Nechť &amp;lt;math&amp;gt;\mathfrak{A}&amp;lt;/math&amp;gt; je struktura s nosičem &amp;lt;math&amp;gt;A&amp;lt;/math&amp;gt; a &amp;lt;math&amp;gt;P\subseteq A&amp;lt;/math&amp;gt;, potom &amp;lt;math&amp;gt;\mathcal{L}(P)&amp;lt;/math&amp;gt; je jazyk obsahující pouze parametry z &amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; a &amp;lt;math&amp;gt;\mathit{Form^n_{\mathcal{L}(P)}}&amp;lt;/math&amp;gt; množina formulí &amp;lt;math&amp;gt;\varphi&amp;lt;/math&amp;gt; v jazyce &amp;lt;math&amp;gt;\mathcal{L}(P)&amp;lt;/math&amp;gt; kde &amp;lt;math&amp;gt;\varphi&amp;lt;/math&amp;gt; má právě &amp;lt;math&amp;gt;n&amp;lt;/math&amp;gt; proměnných.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| '''Definice:''' Nechť &amp;lt;math&amp;gt;\mathfrak{A}&amp;lt;/math&amp;gt; je struktura s nosičem &amp;lt;math&amp;gt;A&amp;lt;/math&amp;gt; a &amp;lt;math&amp;gt;P\subseteq A&amp;lt;/math&amp;gt;, potom &amp;lt;math&amp;gt;\mathcal{L}(P)&amp;lt;/math&amp;gt; je jazyk obsahující pouze parametry z &amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; a &amp;lt;math&amp;gt;\mathit{Form^n_{\mathcal{L}(P)}}&amp;lt;/math&amp;gt; množina formulí &amp;lt;math&amp;gt;\varphi&amp;lt;/math&amp;gt; v jazyce &amp;lt;math&amp;gt;\mathcal{L}(P)&amp;lt;/math&amp;gt; kde &amp;lt;math&amp;gt;\varphi&amp;lt;/math&amp;gt; má právě &amp;lt;math&amp;gt;n&amp;lt;/math&amp;gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;volných &lt;/ins&gt;proměnných.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|}&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|}&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Na množině &amp;lt;math&amp;gt;\mathit{Form^n_{\mathcal{L}(P)}}&amp;lt;/math&amp;gt; můžeme opět zavést ekvivalenci &amp;lt;math&amp;gt;\equiv_T&amp;lt;/math&amp;gt; jako výše v ''Konstrukci''. Zadefinujeme-li také &amp;lt;math&amp;gt;\equiv_T&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;\wedge&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;\vee&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;-&amp;lt;/math&amp;gt;,&amp;lt;math&amp;gt;\textbf{0}&amp;lt;/math&amp;gt; a &amp;lt;math&amp;gt;\textbf{1}&amp;lt;/math&amp;gt; jako v ''Konstrukci'' výše a zvolíme &amp;lt;math&amp;gt;T=Th(\mathfrak{A})&amp;lt;/math&amp;gt; získáme [[Booleova algebra|Booleovu algebru]], jež značíme &amp;lt;math&amp;gt;\mathcal{L}_n(P,\mathfrak{A})&amp;lt;/math&amp;gt;.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Na množině &amp;lt;math&amp;gt;\mathit{Form^n_{\mathcal{L}(P)}}&amp;lt;/math&amp;gt; můžeme opět zavést ekvivalenci &amp;lt;math&amp;gt;\equiv_T&amp;lt;/math&amp;gt; jako výše v ''Konstrukci''. Zadefinujeme-li také &amp;lt;math&amp;gt;\equiv_T&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;\wedge&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;\vee&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;-&amp;lt;/math&amp;gt;,&amp;lt;math&amp;gt;\textbf{0}&amp;lt;/math&amp;gt; a &amp;lt;math&amp;gt;\textbf{1}&amp;lt;/math&amp;gt; jako v ''Konstrukci'' výše a zvolíme &amp;lt;math&amp;gt;T=Th(\mathfrak{A})&amp;lt;/math&amp;gt; získáme [[Booleova algebra|Booleovu algebru]], jež značíme &amp;lt;math&amp;gt;\mathcal{L}_n(P,\mathfrak{A})&amp;lt;/math&amp;gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>HonzaB</name></author>
		
	</entry>
	<entry>
		<id>https://wikisofia.cz/w/index.php?title=Lindenbaum-Tarsk%C3%A9ho_algebry&amp;diff=8881&amp;oldid=prev</id>
		<title>Veronika.Kovrzkova: /* \mathcal{L}_n(P,\mathfrak{A}) */</title>
		<link rel="alternate" type="text/html" href="https://wikisofia.cz/w/index.php?title=Lindenbaum-Tarsk%C3%A9ho_algebry&amp;diff=8881&amp;oldid=prev"/>
		<updated>2014-11-18T20:19:59Z</updated>

		<summary type="html">&lt;p&gt;&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;\mathcal{L}_n(P,\mathfrak{A})&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;cs&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;← Starší verze&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;Verze z 18. 11. 2014, 20:19&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l60&quot; &gt;Řádek 60:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Řádek 60:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;'''Význam:''' Vzhledem k tomu, že každá &amp;lt;math&amp;gt;[\varphi]_{\equiv_T}&amp;lt;/math&amp;gt; z &amp;lt;math&amp;gt;\mathcal{L}_n(P,\mathfrak{A})&amp;lt;/math&amp;gt; definuje právě jednu &amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt;-definovatelnou množinu v &amp;lt;math&amp;gt;A^n&amp;lt;/math&amp;gt; nepřekvapí nás, že platí:&amp;lt;br/&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;'''Význam:''' Vzhledem k tomu, že každá &amp;lt;math&amp;gt;[\varphi]_{\equiv_T}&amp;lt;/math&amp;gt; z &amp;lt;math&amp;gt;\mathcal{L}_n(P,\mathfrak{A})&amp;lt;/math&amp;gt; definuje právě jednu &amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt;-definovatelnou množinu v &amp;lt;math&amp;gt;A^n&amp;lt;/math&amp;gt; nepřekvapí nás, že platí:&amp;lt;br/&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;math&amp;gt;\mathcal{L}_n(P,\mathfrak{A})\cong\mathbb{B}_n(P,\mathfrak{A})&amp;lt;/math&amp;gt;&amp;lt;br/&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;math&amp;gt;\mathcal{L}_n(P,\mathfrak{A})\cong\mathbb{B}_n(P,\mathfrak{A})&amp;lt;/math&amp;gt;&amp;lt;br/&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;kde &amp;lt;math&amp;gt;\mathbb{B}_n(P,\mathfrak{A}&amp;lt;/math&amp;gt; je algebra množin s nosičem &amp;lt;math&amp;gt;B_n(P,\mathfrak{A})&amp;lt;/math&amp;gt;.&amp;lt;ref&amp;gt;A Shorten Model Theory, Wilfred Hodges, Cambridge UP, April 1997&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;kde &amp;lt;math&amp;gt;\mathbb{B}_n(P,\mathfrak{A}&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;)&lt;/ins&gt;&amp;lt;/math&amp;gt; je &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;[[Algebra množin|&lt;/ins&gt;algebra množin&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;]] &lt;/ins&gt;s nosičem &amp;lt;math&amp;gt;B_n(P,\mathfrak{A})&amp;lt;/math&amp;gt;.&amp;lt;ref&amp;gt;A Shorten Model Theory, Wilfred Hodges, Cambridge UP, April 1997&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Algebra &amp;lt;math&amp;gt;\mathbb{B}_n(P,\mathfrak{A})&amp;lt;/math&amp;gt; slouží k definici &amp;lt;math&amp;gt;n&amp;lt;/math&amp;gt;-typu v [[Teorie modelů|Teorii modelů]] a důkazu [[Morleyova věta|Morleyovy věty]].&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Algebra &amp;lt;math&amp;gt;\mathbb{B}_n(P,\mathfrak{A})&amp;lt;/math&amp;gt; slouží k definici &amp;lt;math&amp;gt;n&amp;lt;/math&amp;gt;-typu v [[Teorie modelů|Teorii modelů]] a důkazu [[Morleyova věta|Morleyovy věty]].&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Veronika.Kovrzkova</name></author>
		
	</entry>
	<entry>
		<id>https://wikisofia.cz/w/index.php?title=Lindenbaum-Tarsk%C3%A9ho_algebry&amp;diff=8880&amp;oldid=prev</id>
		<title>Veronika.Kovrzkova: /* \mathcal{L}_n(P,\mathfrak{A}) */</title>
		<link rel="alternate" type="text/html" href="https://wikisofia.cz/w/index.php?title=Lindenbaum-Tarsk%C3%A9ho_algebry&amp;diff=8880&amp;oldid=prev"/>
		<updated>2014-11-18T20:18:19Z</updated>

		<summary type="html">&lt;p&gt;&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;\mathcal{L}_n(P,\mathfrak{A})&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;cs&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;← Starší verze&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;Verze z 18. 11. 2014, 20:18&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l58&quot; &gt;Řádek 58:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Řádek 58:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|}&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|}&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;'''Význam:''' Vzhledem k tomu, že každá &amp;lt;math&amp;gt;[\varphi]_{\equiv_T}&amp;lt;/math&amp;gt; z &amp;lt;math&amp;gt;\mathcal{L}_n(P,\mathfrak{A})&amp;lt;/math&amp;gt; definuje právě jednu &amp;lt;math&amp;gt;P&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;$&lt;/del&gt;&amp;lt;/math&amp;gt;definovatelnou množinu v &amp;lt;math&amp;gt;A^n&amp;lt;/math&amp;gt; nepřekvapí nás, že platí:&amp;lt;br/&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;'''Význam:''' Vzhledem k tomu, že každá &amp;lt;math&amp;gt;[\varphi]_{\equiv_T}&amp;lt;/math&amp;gt; z &amp;lt;math&amp;gt;\mathcal{L}_n(P,\mathfrak{A})&amp;lt;/math&amp;gt; definuje právě jednu &amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;-&lt;/ins&gt;definovatelnou množinu v &amp;lt;math&amp;gt;A^n&amp;lt;/math&amp;gt; nepřekvapí nás, že platí:&amp;lt;br/&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;math&amp;gt;\mathcal{L}_n(P,\mathfrak{A})\cong\mathbb{B}_n(P,\mathfrak{A})&amp;lt;/math&amp;gt;&amp;lt;br/&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;math&amp;gt;\mathcal{L}_n(P,\mathfrak{A})\cong\mathbb{B}_n(P,\mathfrak{A})&amp;lt;/math&amp;gt;&amp;lt;br/&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;kde &amp;lt;math&amp;gt;\mathbb{B}_n(P,\mathfrak{A}&amp;lt;/math&amp;gt; je algebra množin s nosičem &amp;lt;math&amp;gt;B_n(P,\mathfrak{A})&amp;lt;/math&amp;gt;.&amp;lt;ref&amp;gt;A Shorten Model Theory, Wilfred Hodges, Cambridge UP, April 1997&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;kde &amp;lt;math&amp;gt;\mathbb{B}_n(P,\mathfrak{A}&amp;lt;/math&amp;gt; je algebra množin s nosičem &amp;lt;math&amp;gt;B_n(P,\mathfrak{A})&amp;lt;/math&amp;gt;.&amp;lt;ref&amp;gt;A Shorten Model Theory, Wilfred Hodges, Cambridge UP, April 1997&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Algebra &amp;lt;math&amp;gt;\mathbb{B}_n(P,\mathfrak{A})&amp;lt;/math&amp;gt; slouží k definici &amp;lt;math&amp;gt;n&amp;lt;/math&amp;gt;-typu v [[Teorie modelů|Teorii modelů]] a důkazu [[Morleyova věta|Morleyovy věty]].&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Algebra &amp;lt;math&amp;gt;\mathbb{B}_n(P,\mathfrak{A})&amp;lt;/math&amp;gt; slouží k definici &amp;lt;math&amp;gt;n&amp;lt;/math&amp;gt;-typu v [[Teorie modelů|Teorii modelů]] a důkazu [[Morleyova věta|Morleyovy věty]].&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt; &lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Odkazy ==&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Odkazy ==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;=== Reference ===&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;=== Reference ===&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Veronika.Kovrzkova</name></author>
		
	</entry>
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