English

Ultrafilters in the random real model

Logic 2025-09-18 v2

Abstract

We prove that \textsf{P}-points (even strong P-points) and Gruff ultrafilters exist in any forcing extension obtained by adding fewer than ω\aleph_{\omega}% -many random reals to a model of \textsf{CH. }These results improve and correct previous theorems that can be found in the literature.

Keywords

Cite

@article{arxiv.2507.08346,
  title  = {Ultrafilters in the random real model},
  author = {Alan Dow and Osvaldo Guzmán},
  journal= {arXiv preprint arXiv:2507.08346},
  year   = {2025}
}
R2 v1 2026-07-01T03:56:05.284Z