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 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