On the cofinality of the least λ-strongly compact cardinal

You, Zhixing and Yuan, Jiachen (2024) On the cofinality of the least λ-strongly compact cardinal. Journal of Symbolic Logic, 89 (2). pp. 569-582. ISSN 0022-4812

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In this paper, we characterize the possible cofinalities of the least λ-strongly compact cardinal.We show that, on the one hand, for any regular cardinal, δ, that carries a λ-complete uniform ultrafilter, it is consistent, relative to the existence of a supercompact cardinal above δ, that the least λ-strongly compact cardinal has cofinality δ. On the other hand, provably the cofinality of the least λ-strongly compact cardinal always carries a λ-complete uniform ultrafilter.

Item Type: Article
Additional Information: Funding Information: During the work, the first author was supported by NSFC No. 11871464 until July 2022 and the China Scholarship Council (No. 202004910742) from October 2020 to October 2021. The first author was also supported by the European Research Council (grant agreement ERC-2018-StG 802756) from July 2022. The second author was supported by UKRI Future Leaders Fellowship [MR/T021705/2].
Uncontrolled Keywords: cofinality,iterated ultrapower,radin forcing,λ-strongly compact cardinal,03e35 03e55,logic,philosophy ,/dk/atira/pure/subjectarea/asjc/2600/2609
Faculty \ School: Faculty of Science > School of Mathematics
UEA Research Groups: Faculty of Science > Research Groups > Logic
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Depositing User: LivePure Connector
Date Deposited: 20 Feb 2023 15:30
Last Modified: 29 May 2024 08:30
URI: https://ueaeprints.uea.ac.uk/id/eprint/91204
DOI: 10.1017/jsl.2023.4


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