Sigma-Prikry forcing III: Down to Aleph_omega

Alejandro Poveda; Assaf Rinot; Dima Sinapova

Sigma-Prikry forcing III: Down to Aleph_omega

Logic 2022-09-22 v1

Authors: Alejandro Poveda , Assaf Rinot , Dima Sinapova

Abstract

We prove the consistency of the failure of the singular cardinals hypothesis at $\aleph_\omega$ together with the reflection of all stationary subsets of $\aleph_{\omega+1}$ . This shows that two classic results of Magidor (from 1977 and 1982) can hold simultaneously.

Cite

@article{arxiv.2209.10501,
  title  = {Sigma-Prikry forcing III: Down to Aleph_omega},
  author = {Alejandro Poveda and Assaf Rinot and Dima Sinapova},
  journal= {arXiv preprint arXiv:2209.10501},
  year   = {2022}
}