A note on $\delta$-strongly compact cardinals

Abstract

In this paper we investigate more characterizations and applications of $\delta$-strongly compact cardinals. We show that, for a cardinal $\kappa$ the following are equivalent: (1) $\kappa$ is $\delta$-strongly compact, (2) For every regular $\lambda \ge \kappa$ there is a $\delta$-complete uniform ultrafilter over $\lambda$, and (3) Every product space of $\delta$-Lindelöf spaces is $\kappa$-Lindelöf. We also prove that in the Cohen forcing extension, the least ${\omega }_1$-strongly compact cardinal is a precise upper bound on the tightness of the products of two countably tight spaces.

arXiv admin note: text overlap with arXiv:1709.07991