Universal wide Aronszajn tree

Abstract

A wide Aronszajn tree is a tree of size ${\aleph }_1$ with no uncountable branches. Assuming the consistency of the existence of a weakly compact cardinal, we show the consistency of the existence of a wide Aronszajn tree that is \textit{universal} in the sense that it contains an isomorphic copy of every wide Aronszajn tree.