Ketonen's question and other cardinal sins
Logic
2025-12-01 v2
Abstract
Answering a question of Ketonen from the late 1970's, it is proved that a weakly compact cardinal carrying an indecomposable ultrafilter need not be measurable. The result is obtained by analyzing the limit of a decreasing sequence of models of ZFC. The utility of this proof technique is demonstrated further in this paper, where a problem by Bagaria and Magidor concerning strong compactness, and a problem by Lambie-Hanson and Rinot concerning the -sequence number are solved as well.
Keywords
Cite
@article{arxiv.2408.01547,
title = {Ketonen's question and other cardinal sins},
author = {Assaf Rinot and Zhixing You and Jiachen Yuan},
journal= {arXiv preprint arXiv:2408.01547},
year = {2025}
}
Comments
Corrections upon feedback from Tom Benhamou