Proper and Improper Variants of Mathias and Silver Forcing

Shixiao Liu

Proper and Improper Variants of Mathias and Silver Forcing

Logic 2025-07-25 v3

Authors: Shixiao Liu

Abstract

In this paper we answer several questions in arXiv:2102.06009 regarding density variants of Mathias and Silver forcing. These questions include whether each of the forcing is proper, add dominating real, or add Cohen real. We also generalize one of the proofs to Mathias forcings parametrized by lower semi-continuous submeasures satisfying certain properties.

Keywords

set theory forcing

Cite

@article{arxiv.2311.01005,
  title  = {Proper and Improper Variants of Mathias and Silver Forcing},
  author = {Shixiao Liu},
  journal= {arXiv preprint arXiv:2311.01005},
  year   = {2025}
}