On the cofinality of the least λ-strongly compact cardinal

Zhixing You, Jiachen Yuan

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    Abstract

    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.

    Original languageEnglish
    Pages (from-to)569-582
    Number of pages14
    JournalJournal of Symbolic Logic
    Volume89
    Issue number2
    Early online date19 Jan 2023
    DOIs
    Publication statusPublished - Jun 2024

    Keywords

    • Cofinality
    • Iterated ultrapower
    • Radin forcing
    • λ-strongly compact cardinal
    • 03E35 03E55

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