Partial strong compactness and squares

Yair Hayut

doi:10.4064/fm626-9-2018

Partial strong compactness and squares

Yair Hayut^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

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^<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.

Original language	English
Pages (from-to)	193-204
Number of pages	12
Journal	Fundamenta Mathematicae
Volume	246
Issue number	2
DOIs	https://doi.org/10.4064/fm626-9-2018
State	Published - 2019
Externally published	Yes

Bibliographical note

Publisher Copyright:
© Instytut Matematyczny PAN, 2019

Keywords

Infinitary logic
Strong compactness

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10.4064/fm626-9-2018

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Partial strong compactness and squares

Abstract

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Keywords

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