English

Guessing models imply the singular cardinal hypothesis

Logic 2019-07-23 v2

Abstract

In this article we prove three main theorems: (1) guessing models are internally unbounded, (2) for any regular cardinal κω2\kappa \ge \omega_2, ISP(κ)\textsf{ISP}(\kappa) implies that SCH\textsf{SCH} holds above κ\kappa, and (3) forcing posets which have the ω1\omega_1-approximation property also have the countable covering property. These results solve open problems of Viale and Hachtman-Sinapova.

Keywords

Cite

@article{arxiv.1903.10476,
  title  = {Guessing models imply the singular cardinal hypothesis},
  author = {John Krueger},
  journal= {arXiv preprint arXiv:1903.10476},
  year   = {2019}
}
R2 v1 2026-06-23T08:18:32.951Z