Kurepa tree
In set theory, a Kurepa tree is a tree (T, <) of height ω1, each of whose levels is at most countable, and has at least ℵ2 many branches. This concept was introduced by Kurepa . The existence of a Kurepa tree (known as the Kurepa hypothesis, though Kurepa originally conjectured that this was false) is consistent with the axioms of ZFC: Solovay showed in unpublished work that there are Kurepa trees in Gödel's constructible universe . More precisely, the existence of Kurepa trees follows from the diamond plus principle, which holds in the constructible universe. On the other hand, Silver showed that if a strongly inaccessible cardinal is Lévy collapsed to ω2 then, in the resulting model, there are no Kurepa trees. The existence of an inaccessible cardinal is in fact equiconsistent wit
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Kurepa tree
In set theory, a Kurepa tree is a tree (T, <) of height ω1, each of whose levels is at most countable, and has at least ℵ2 many branches. This concept was introduced by Kurepa . The existence of a Kurepa tree (known as the Kurepa hypothesis, though Kurepa originally conjectured that this was false) is consistent with the axioms of ZFC: Solovay showed in unpublished work that there are Kurepa trees in Gödel's constructible universe . More precisely, the existence of Kurepa trees follows from the diamond plus principle, which holds in the constructible universe. On the other hand, Silver showed that if a strongly inaccessible cardinal is Lévy collapsed to ω2 then, in the resulting model, there are no Kurepa trees. The existence of an inaccessible cardinal is in fact equiconsistent wit
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Hipoteza Kurepy, KH (od ang. K ...... ć na gruncie tych aksjomatów).
@pl
In set theory, a Kurepa tree i ...... pa tree unless κ is ineffable.
@en
集合論において、クレパ木とは高さ の木(T, <)であって、 ...... 能基数の存在とクレパの仮説の否定はであることが知られている。
@ja
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Hipoteza Kurepy, KH (od ang. K ...... ć na gruncie tych aksjomatów).
@pl
In set theory, a Kurepa tree i ...... is in fact equiconsistent wit
@en
集合論において、クレパ木とは高さ の木(T, <)であって、 ...... 能基数の存在とクレパの仮説の否定はであることが知られている。
@ja
label
Hipoteza Kurepy
@pl
Kurepa tree
@en
クレパ木
@ja