A note on δ-strongly compact cardinals

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3 Citations (Scopus)

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 an exact upper bound on the tightness of the products of two countably tight spaces.

Original languageEnglish
Article number107538
JournalTopology and its Applications
Volume301
DOIs
Publication statusPublished - 2021 Sept 1

Keywords

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

ASJC Scopus subject areas

  • Geometry and Topology

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