Square Compactness and the filter extension property

2019/09/12 by Buhagiar, David, Džamonja, Mirna
#54D20 #FOS: Mathematics #General Topology (math.GN) #Logic (math.LO) #Primary 03E55 #Secondary 54F05

paper · doi:10.48550/arxiv.1909.05474

Abstract

We show that the consistency strength of κ being 2^κ-square compact is at least weak compact and strictly less than indescribable. This is the first known improvement to the upper bound of strong compactness obtained in 1973 by Hajnal and Juh' asz.

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• Squares, ultrafilters and forcing axioms
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• Compactness and Comparison