# 2018 seminar talk: Special $\aleph_2$-Aronszajn trees and GCH

Talk held by David Asperó (University of East Anglia, Norwich, UK) at the KGRC seminar on 2018-10-22.

### Abstract

In joint work with Mohammad Golshani, and assuming the existence of a weakly compact cardinal, we build a forcing extension in which GCH holds and every $\aleph_2$-Aronszajn tree is special. This answers a well-known question from the 1970’s. I will give the proof of this theorem, with as many details as possible.

Note: Recordings of this talk are available on YouTube: part 1, part 2