English

How far is almost strong compactness from strong compactness

Logic 2023-02-28 v1

Abstract

Bagaria and Magidor introduced the notion of almost strong compactness, which is very close to the notion of strong compactness. Boney and Brooke-Taylor asked whether the least almost strongly compact cardinal is strongly compact. Goldberg gives a positive answer in the case SCH\mathrm{SCH} holds from below and the least almost strongly compact cardinal has uncountable cofinality. In this paper, we give a negative answer for the general case. Our result also gives an affirmative answer to a question of Bagaria and Magidor.

Cite

@article{arxiv.2302.13171,
  title  = {How far is almost strong compactness from strong compactness},
  author = {Zhixing You and Jiachen Yuan},
  journal= {arXiv preprint arXiv:2302.13171},
  year   = {2023}
}

Comments

14 pages

R2 v1 2026-06-28T08:49:36.160Z