In set theory, an Aronszajn tree is an uncountable tree with no uncountable branches and no uncountable levels. For example, every Suslin tree is an Aronszajn tree. More generally, for a cardinal κ, a κ-Aronszajn tree is a tree of cardinality κ in which all levels have size less than κ and all branches have height less than κ (so Aronszajn trees are the same as -Aronszajn trees). They are named for Nachman Aronszajn, who constructed an Aronszajn tree in 1934; his construction was described by .