The effect of forcing axioms on the tightness of the gδ-modification

William Chen-Mertens, Paul J. Szeptycki

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We show that PFA implies that the tightness t(Xδ) of the Gδ-modification of a Fréchet α1-space X is at most ω1, while (κ) implies that there is a Fréchet α1-space with Gδ-tightness equal to κ. We use the example constructed from (κ) to show that a local version of the bound t(Xδ) ≤ 2t(X)L(X) does not hold. We also construct, assuming MA, an example of a Fréchet space whose Gδ-tightness is larger than ω1.

Original languageEnglish
Pages (from-to)195-202
Number of pages8
JournalFundamenta Mathematicae
Volume251
Issue number2
DOIs
StatePublished - 1 Jan 2020
Externally publishedYes

Keywords

  • Fréchet-Urysohn
  • G-modification
  • PFA
  • Square principles
  • Tightness
  • α1-spaces

ASJC Scopus subject areas

  • Algebra and Number Theory

Fingerprint

Dive into the research topics of 'The effect of forcing axioms on the tightness of the gδ-modification'. Together they form a unique fingerprint.

Cite this