TITLE: $GCH$ and special Aronszajn trees
QUESTION [15 upvotes]: Question. Does $\text{GCH}$ imply the existence of a non-special $\aleph_2$-Aronszajn tree ?

Remark 1. By a result of Jensen, it is consistent that $\text{GCH}$ holds and all $\aleph_1$-Aronszajn trees are special.
Remark 2. The above question is related to the famous question ``does $\text{GCH}$ imply the existence of an $\aleph_2$-Souslin tree ?''.

REPLY [5 votes]: It turned out the answer to the question is no.
David Aspero and I, have proved the following:
Theorem. Assuming the existence of a weakly compact cardinal, there exists a generic extension of the universe in which $GCH$ holds and all $\aleph_2$-Aronszajn trees are special.
See The special Aronszajn tree property at $\aleph_2$ and $GCH$.

Comments and suggestions on the paper are welcome.