English

A forcing axiom deciding the generalized Souslin Hypothesis

Logic 2019-08-15 v2

Abstract

We derive a forcing axiom from the conjunction of square and diamond, and present a few applications, primary among them being the existence of super-Souslin trees. It follows that for every uncountable cardinal λ\lambda, if λ++\lambda^{++} is not a Mahlo cardinal in G\"odel's constructible universe, then 2λ=λ+2^\lambda = \lambda^+ entails the existence of a λ+\lambda^+-complete λ++\lambda^{++}-Souslin tree.

Keywords

Cite

@article{arxiv.1708.06932,
  title  = {A forcing axiom deciding the generalized Souslin Hypothesis},
  author = {Chris Lambie-Hanson and Assaf Rinot},
  journal= {arXiv preprint arXiv:1708.06932},
  year   = {2019}
}
R2 v1 2026-06-22T21:21:31.129Z