A Small Ultrafilter Number at Every Singular Cardinal
Logic
2025-12-10 v2
Abstract
We obtain a small ultrafilter number at . Moreover, we develop a version of the overlapping strong extender forcing with collapses which can keep the top cardinal inaccessible. We apply this forcing to construct a model where is the least inaccessible and is a model of GCH at regulars, failures of SCH at singulars, and the ultrafilter numbers at all singulars are small.
Keywords
Cite
@article{arxiv.2302.07311,
title = {A Small Ultrafilter Number at Every Singular Cardinal},
author = {Tom Benhamou and Sittinon Jirattikansakul},
journal= {arXiv preprint arXiv:2302.07311},
year = {2025}
}