Joint work with Zhixing You and Jiachen Yuan.
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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Submitted to Israel Journal of Mathematics, November 2024.
Accepted June 2025.