Polytope model: Difference between revisions

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In [[set theory]], a '''Kurepa tree''' is a [[tree (set theory)|tree]] (''T'',&nbsp;<) of height <math>\omega_1</math>, each of whose levels is at most countable, and has at least <math>\aleph_2</math> many branches. It was named after [[Yugoslavia|Yugoslav]] mathematician [[Đuro Kurepa]]. The existence of a Kurepa tree (known as the '''Kurepa hypothesis''') is consistent with the axioms of [[ZFC]]: As [[Robert M. Solovay|Solovay]] showed, there are Kurepa trees in [[Kurt Gödel|Gödel]]'s [[constructible universe]]. On the other hand, as [[Jack Silver|Silver]] proved in 1971, if a [[strongly inaccessible cardinal]] is [[List of forcing notions#Levy collapsing|Lévy collapsed]] to <math>\omega_2</math> then, in the resulting model, there are no Kurepa trees.  
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== See also ==
* [[Aronszajn tree]]
* [[Suslin tree]]
 
== References ==
* {{cite book|author=Jech, Thomas|title=Set Theory|publisher=Springer-Verlag|year=2002|isbn=3-540-44085-2}}
 
[[Category:Trees (set theory)]]
 
{{settheory-stub}}

Latest revision as of 20:14, 3 July 2014

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