Ketonen's question and other cardinal sins

Assaf Rinot; Zhixing You; Jiachen Yuan

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arXiv · 2408.01547

Ketonen's question and other cardinal sins

Assaf Rinot·Zhixing You·Jiachen Yuan

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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 $C$-sequence number are solved as well.

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BibTeX RIS

Assaf Rinot, Zhixing You, Jiachen Yuan. 2024-08-02. Ketonen's question and other cardinal sins. https://arxiv.org/abs/2408.01547

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