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

William Chen-Mertens; Paul J. Szeptycki

doi:10.4064/fm869-2-2020

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

William Chen-Mertens, Paul J. Szeptycki

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

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

Original language	English
Pages (from-to)	195-202
Number of pages	8
Journal	Fundamenta Mathematicae
Volume	251
Issue number	2
DOIs	https://doi.org/10.4064/fm869-2-2020
State	Published - 1 Jan 2020
Externally published	Yes

Keywords

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

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.4064/fm869-2-2020

Cite this

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abstract = "We show that PFA implies that the tightness t(Xδ) of the Gδ-modification of a Fr{\'e}chet α1-space X is at most ω1, while (κ) implies that there is a Fr{\'e}chet 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 Fr{\'e}chet space whose Gδ-tightness is larger than ω1.",

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