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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