Partial strong compactness and squares [article]

Yair Hayut
2018 arXiv   pre-print
In this paper 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 L_κ,κ. Using this equivalence we show that if any κ-complete filter on λ can be extended to a κ-complete ultrafilter and λ^<κ = λ then (μ) fails for all regular μ∈[κ,2^λ]. As an application, we improve the lower bound for the consistency strength of κ-compactness, a case which was explicitly considered by Mitchell.
arXiv:1804.05758v2 fatcat:c35yjf22sjds5bnyvyunxhj2da