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	<id>https://en.formulasearchengine.com/w/index.php?action=history&amp;feed=atom&amp;title=Polytope_model</id>
	<title>Polytope model - Revision history</title>
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	<updated>2026-10-20T12:29:09Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
	<generator>MediaWiki 1.47.0-wmf.7</generator>
	<entry>
		<id>https://en.formulasearchengine.com/w/index.php?title=Polytope_model&amp;diff=251875&amp;oldid=prev</id>
		<title>en&gt;Frietjes: cleanup (wikitables, html markup, layout, etc.)</title>
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		<updated>2014-07-03T18:14:42Z</updated>

		<summary type="html">&lt;p&gt;cleanup (wikitables, html markup, layout, etc.)&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw-interface=&quot;&quot;&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 20:14, 3 July 2014&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-l1&quot;&gt;Line 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; 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;In [[set theory]], &lt;/del&gt;a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&#039;&#039;&#039;Kurepa tree&#039;&#039;&#039; &lt;/del&gt;is &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;a &lt;/del&gt;[&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[tree (set theory)|tree]] (&#039;&#039;T&#039;&#039;,&amp;amp;nbsp;&amp;lt;) of height &amp;lt;math&amp;gt;\omega_1&amp;lt;&lt;/del&gt;/&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;math&amp;gt;, each of whose levels is at most countable, and has at least &amp;lt;math&amp;gt;\aleph_2&amp;lt;&lt;/del&gt;/&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;math&amp;gt; many branches&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;It was named after [[Yugoslavia|Yugoslav]&lt;/del&gt;] &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;mathematician &lt;/del&gt;[&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[Đuro Kurepa]&lt;/del&gt;]. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;The existence of a Kurepa tree (known as the &#039;&#039;&#039;Kurepa hypothesis&#039;&#039;&#039;) &lt;/del&gt;is &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;consistent with the axioms of &lt;/del&gt;[&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[ZFC]]&lt;/del&gt;: &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;As [[Robert M&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Solovay|Solovay]] showed, there are Kurepa trees in [[Kurt Gödel|Gödel]]&#039;s [[constructible universe]]&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;On the other hand, as [[Jack Silver|Silver&lt;/del&gt;]&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;] proved in 1971, if a [[strongly inaccessible cardinal]] is [[List &lt;/del&gt;of &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;forcing notions#Levy collapsing|Lévy collapsed]] to &lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;math&lt;/del&gt;&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;\omega_2&lt;/del&gt;&amp;lt;/&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;math&amp;gt; then, in the resulting model, there are no Kurepa trees&lt;/del&gt;.  &lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; 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;I am Oscar and I totally dig that title. Hiring is my occupation. It&#039;s not &lt;/ins&gt;a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;typical factor but what she likes doing &lt;/ins&gt;is [&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;http:&lt;/ins&gt;//&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Www.Herpes&lt;/ins&gt;.&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;org/smart-living-with-genital-herpes/ foundation leaping&lt;/ins&gt;] &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; &lt;/ins&gt;[&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;http://www.pinaydiaries.com/blog/104745 at home std test&lt;/ins&gt;] &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;home std testing and now she is attempting to make money with it&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;South Dakota &lt;/ins&gt;is &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;her beginning place but she &lt;/ins&gt;[&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;http&lt;/ins&gt;:&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;//Std-Clinics&lt;/ins&gt;.&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Findthebest&lt;/ins&gt;.&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;com/ requirements&lt;/ins&gt;] &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;to transfer because &lt;/ins&gt;of &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;her family.&lt;/ins&gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/ins&gt;&amp;gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&amp;gt;Feel free to surf to my web blog:  std testing [http:&lt;/ins&gt;/&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;/www.innovec&lt;/ins&gt;.&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;com/node/3171 at home std testing&lt;/ins&gt;] &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;home home std test kit (&lt;/ins&gt;[&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;http://www.eyelevelfederalway.com/xe/index.php?mid&lt;/ins&gt;=&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Promotions&amp;amp;page&lt;/ins&gt;=&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;1&amp;amp;document_srl&lt;/ins&gt;=&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;571267 Learn Additional]&lt;/ins&gt;)&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; 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;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; 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;== See also ==&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; 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;* [[Aronszajn tree&lt;/del&gt;]&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;]&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; 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;* &lt;/del&gt;[&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[Suslin tree]]&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; 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;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; 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;References &lt;/del&gt;=&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;=&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; 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;* {{cite book|author=Jech, Thomas|title=Set Theory|publisher=Springer-Verlag|year=2002|isbn=3-540-44085-2}}&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; 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;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; 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;[[Category:Trees (set theory&lt;/del&gt;)&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;]]&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; 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;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; 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;{{settheory-stub}}&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>en&gt;Frietjes</name></author>
	</entry>
	<entry>
		<id>https://en.formulasearchengine.com/w/index.php?title=Polytope_model&amp;diff=15731&amp;oldid=prev</id>
		<title>en&gt;Addbot: Bot: Migrating 1 interwiki links, now provided by Wikidata on d:q1681391</title>
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		<updated>2013-03-16T10:59:49Z</updated>

		<summary type="html">&lt;p&gt;&lt;a href=&quot;/w/index.php?title=User:Addbot&amp;amp;action=edit&amp;amp;redlink=1&quot; class=&quot;new&quot; title=&quot;User:Addbot (page does not exist)&quot;&gt;Bot:&lt;/a&gt; Migrating 1 interwiki links, now provided by &lt;a href=&quot;https://en.wikipedia.org/wiki/Wikidata&quot; class=&quot;extiw&quot; title=&quot;wikipedia:Wikidata&quot;&gt;Wikidata&lt;/a&gt; on &lt;a href=&quot;/w/index.php?title=D:q1681391&amp;amp;action=edit&amp;amp;redlink=1&quot; class=&quot;new&quot; title=&quot;D:q1681391 (page does not exist)&quot;&gt;d:q1681391&lt;/a&gt;&lt;/p&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 12:59, 16 March 2013&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-l1&quot;&gt;Line 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; 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;Hello&lt;/del&gt;, &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;my title &lt;/del&gt;is &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Andrew &lt;/del&gt;and &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;my spouse doesn&#039;t like it &lt;/del&gt;at &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;all&lt;/del&gt;. The &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;favorite pastime for him and his children &lt;/del&gt;is &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;to perform lacross and he&#039;ll be beginning some thing else alongside &lt;/del&gt;with &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;it&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;For many years he&lt;/del&gt;&#039;s &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;been residing &lt;/del&gt;in &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Alaska and he doesn&#039;t plan on changing it. Credit authorising &lt;/del&gt;is &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;how he makes cash.&lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/del&gt;&amp;gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/del&gt;&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Feel [http://formalarmour&lt;/del&gt;.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;com/index.php?do&lt;/del&gt;=&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;/profile-26947/info/ free psychic readings&lt;/del&gt;] &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;to surf to my homepage; &lt;/del&gt;[&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;http://www.january&lt;/del&gt;-&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;yjm.com/xe/index.php?mid&lt;/del&gt;=&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;video&amp;amp;document_srl&lt;/del&gt;=&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;158289 love psychics] online (&lt;/del&gt;[&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;http&lt;/del&gt;:&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;//ustanford.com/index.php?do=/profile&lt;/del&gt;-&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;38218/info/ mouse click the following web page])&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; 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;In [[set theory]], a &#039;&#039;&#039;Kurepa tree&#039;&#039;&#039; is a [[tree (set theory)|tree]] (&#039;&#039;T&#039;&#039;,&amp;amp;nbsp;&amp;lt;) of height &amp;lt;math&amp;gt;\omega_1&amp;lt;/math&amp;gt;&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;each of whose levels &lt;/ins&gt;is &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;at most countable, &lt;/ins&gt;and &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;has &lt;/ins&gt;at &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;least &amp;lt;math&amp;gt;\aleph_2&amp;lt;/math&amp;gt; many branches. It was named after [[Yugoslavia|Yugoslav]] mathematician [[Đuro Kurepa]]&lt;/ins&gt;. The &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;existence of a Kurepa tree (known as the &#039;&#039;&#039;Kurepa hypothesis&#039;&#039;&#039;) &lt;/ins&gt;is &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;consistent &lt;/ins&gt;with &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;the axioms of [[ZFC]]: As [[Robert M&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Solovay|Solovay]] showed, there are Kurepa trees in [[Kurt Gödel|Gödel]]&lt;/ins&gt;&#039;s &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[constructible universe]]. On the other hand, as [[Jack Silver|Silver]] proved &lt;/ins&gt;in &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;1971, if a [[strongly inaccessible cardinal]] &lt;/ins&gt;is &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[List of forcing notions#Levy collapsing|Lévy collapsed]] to &lt;/ins&gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;math&lt;/ins&gt;&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;\omega_2&lt;/ins&gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;/math&lt;/ins&gt;&amp;gt; &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;then, in the resulting model, there are no Kurepa trees&lt;/ins&gt;.  &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; 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;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; 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;== See also =&lt;/ins&gt;=&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; 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;* [[Aronszajn tree]&lt;/ins&gt;]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; 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;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Suslin tree]]&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; 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;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; 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;== References ==&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; 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;* {{cite book|author=Jech, Thomas|title=Set Theory|publisher=Springer&lt;/ins&gt;-&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Verlag|year&lt;/ins&gt;=&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;2002|isbn&lt;/ins&gt;=&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;3-540-44085-2}}&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; 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;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; 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;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Category&lt;/ins&gt;:&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Trees (set theory)]]&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; 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;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; 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;{{settheory&lt;/ins&gt;-&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;stub}}&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>en&gt;Addbot</name></author>
	</entry>
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		<title>en&gt;Saint Aardvark: Add links for loop skewing (Loop Optimizations)</title>
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		<updated>2012-03-03T00:12:30Z</updated>

		<summary type="html">&lt;p&gt;Add links for loop skewing (Loop Optimizations)&lt;/p&gt;
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		<author><name>en&gt;Saint Aardvark</name></author>
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