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
JournalJournal of Symbolic Logic
Early online date19 Jan 2023
DOIs
Publication statusE-pub ahead of print - 19 Jan 2023

Keywords

  • Cofinality
  • Iterated ultrapower
  • Radin forcing
  • λ-strongly compact cardinal

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