Square compactness and the filter extension property
Volume 252 / 2021
Fundamenta Mathematicae 252 (2021), 325-342
MSC: Primary 03E55, 54D20; Secondary 54F05.
DOI: 10.4064/fm787-4-2020
Published online: 31 August 2020
Abstract
We show that the consistency strength of $\kappa $ being $2^\kappa $-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 Juhász.
