A note on δ-strongly compact cardinals

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Abstract

In this paper we investigate more characterizations and applications of δ-strongly compact cardinals. We show that, for a cardinal κ the following are equivalent: (1) κ is δ-strongly compact, (2) For every regular λ ≥ κ there is a δ-complete uniform ultrafilter over λ, and (3) Every product space of δ-Lindelöf spaces is κ-Lindelöf. We also prove that in the Cohen forcing extension, the least ω1-strongly compact cardinal is a precise upper bound on the tightness of the products of two countably tight spaces.

Original languageEnglish
JournalUnknown Journal
Publication statusPublished - 2020 Jan 4

Keywords

  • Countably tight
  • Lindelöf space
  • Uniform ultrafilter
  • δ-strongly compact cardinal
  • ω-strongly compact cardinal

ASJC Scopus subject areas

  • General

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