In set theory

Set theory

Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...

, a Kurepa tree is a tree

Tree (set theory)

In set theory, a tree is a partially ordered set In set theory, a tree is a partially ordered set (poset) In set theory, a tree is a partially ordered set (poset) (T, In set theory, a tree is a partially ordered set (poset) (T, ...

 (T, <) of height , each of whose levels is at most countable, and has at least many branches. It was named after Serbian

Serbs

The Serbs are a South Slavic ethnic group of the Balkans and southern Central Europe. Serbs are located mainly in Serbia, Montenegro and Bosnia and Herzegovina, and form a sizable minority in Croatia, the Republic of Macedonia and Slovenia. Likewise, Serbs are an officially recognized minority in...

 mathematician Đuro Kurepa. The existence of a Kurepa tree (known as the Kurepa hypothesis) is independent of the axioms of ZFC. As Solovay

Robert M. Solovay

Robert Martin Solovay is an American mathematician specializing in set theory.Solovay earned his Ph.D. from the University of Chicago in 1964 under the direction of Saunders Mac Lane, with a dissertation on A Functorial Form of the Differentiable Riemann–Roch theorem...

 showed, there are Kurepa trees in Gödel

Kurt Gödel

Kurt Friedrich Gödel was an Austrian logician, mathematician and philosopher. Later in his life he emigrated to the United States to escape the effects of World War II. One of the most significant logicians of all time, Gödel made an immense impact upon scientific and philosophical thinking in the...

's constructible universe

Constructible universe

In mathematics, the constructible universe , denoted L, is a particular class of sets which can be described entirely in terms of simpler sets. It was introduced by Kurt Gödel in his 1938 paper "The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis"...

. On the other hand, as Silver

Jack Silver

Jack Howard Silver is a set theorist and logician at the University of California, Berkeley. He has made several deep contributions to set theory...

 proved in 1971, if a strongly inaccessible cardinal is Lévy collapsed to then, in the resulting model, there are no Kurepa trees.