Ketonen's question and other cardinal sins
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914172761014272 |
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| author | Rinot, Assaf You, Zhixing Yuan, Jiachen |
| author_facet | Rinot, Assaf You, Zhixing Yuan, Jiachen |
| contents | 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 $C$-sequence number are solved as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_01547 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ketonen's question and other cardinal sins Rinot, Assaf You, Zhixing Yuan, Jiachen Logic 03E05, 03E35, 03E55 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 $C$-sequence number are solved as well. |
| title | Ketonen's question and other cardinal sins |
| topic | Logic 03E05, 03E35, 03E55 |
| url | https://arxiv.org/abs/2408.01547 |