Kurepa influenced set theory mathematics in several ways, including lending his name to the Kurepa tree.

He is also credited with inventing Silver Indiscernibles and generalizing the notion of a Kurepa tree (called Silver's Principle).

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

The existence of a Kurepa tree (known as the Kurepa hypothesis) is consistent with the axioms of ZFC: As Solovay showed, there are Kurepa trees in Gödel's constructible universe.