Kurepa tree

Kurepa tree

In set theory, a Kurepa tree is a tree ("T", <) of height omega_1, each of whose levels is at most countable, and has at least aleph_2 many branches. It was named after Yugoslav mathematician Đuro Kurepa. The existence of a Kurepa tree (known as the Kurepa hypothesis) is independent of the axioms of ZFC. As Solovay showed, there are Kurepa trees in Gödel's constructible universe. On the other hand, as Silver proved in 1971, if a strongly inaccessible cardinal is Lévy collapsed to omega_2 then, in the resulting model, there are no Kurepa trees.

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