Suslin tree

In mathematics, a Suslin tree is a tree of height ω₁ such that every branch and every antichain is at most countable. They are named after Mikhail Yakovlevich Suslin.

Every Suslin tree is an Aronszajn tree.

The existence of a Suslin tree is independent of ZFC, and is equivalent to the existence of a Suslin line (shown by Kurepa (1935)) or a Suslin algebra. The diamond principle, a consequence of V=L, implies that there is a Suslin tree, and Martin's axiom MA(ℵ₁) implies that there are no Suslin trees.