Square Compactness and the filter extension property

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 Juh{\' a}sz.

This version incorporates referee's comments and some new references. No major mathematical changes have been made