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

Abstract: Starting from the existence of a weakly compact cardinal, we build a generic extension of the universe in which $GCH$ holds and all $\aleph_2$-Aronszajn trees are special and hence there are no $\aleph_2$-Souslin trees. This result answers a well-known open question from the 1970's.