Partial strong compactness and squares

Yair Hayut*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


We analyze the connection between some properties of partially strongly compact cardinals: the completion of filters of certain size and instances of the compactness of Lκ,κ. Using this equivalence we show that if any κ-complete filter on λ can be extended to a κ-complete ultrafilter and λ = λ then (µ) fails for all regular µ ∈ [κ, 2λ]. As an application, we improve the lower bound for the consistency strength of κ-compactness, a case which was explicitly considered by Mitchell.

Original languageAmerican English
Pages (from-to)193-204
Number of pages12
JournalFundamenta Mathematicae
Issue number2
StatePublished - 2019
Externally publishedYes

Bibliographical note

Publisher Copyright:
© Instytut Matematyczny PAN, 2019


  • Infinitary logic
  • Strong compactness


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