The special Aronszajn tree property at $\aleph_2$ and $GCH$

David Asperó; Mohammad Golshani

paper

The special Aronszajn tree property at $ℵ_{2}$ and $GC H$

arXiv:1809.07638

Abstract

Starting from the existence of a weakly compact cardinal, we build a generic extension of the universe in which $GC H$ holds and all $ℵ_{2}$ -Aronszajn trees are special and hence there are no $ℵ_{2}$ -Souslin trees. This result answers a well-known open question from the 1970's.

We fixed a few typos and gaps, and added more explanations for some arguments

The special Aronszajn tree property at ℵ2​ and GCH

Abstract

The special Aronszajn tree property at $ℵ_{2}$ and $GC H$