English

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

Logic 2024-04-25 v7

Abstract

Starting from the existence of a weakly compact cardinal, we build a generic extension of the universe in which GCHGCH holds and all 2\aleph_2-Aronszajn trees are special and hence there are no 2\aleph_2-Souslin trees. This result answers a well-known open question from the 1970's.

Keywords

Cite

@article{arxiv.1809.07638,
  title  = {The special Aronszajn tree property at $\aleph_2$ and $GCH$},
  author = {David Asperó and Mohammad Golshani},
  journal= {arXiv preprint arXiv:1809.07638},
  year   = {2024}
}

Comments

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