2019/10/23 by William Chen-Mertens, Chen-Mertens, William, Paul J. Szeptycki +1 · 1 citation
Computer Science · Immunology and Microbiology · Mathematics · #54A20 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #General Topology (math.GN) #HIV Research and Treatment #Logic (math.LO)
paper · pdf · doi:10.48550/arxiv.1910.10629
openalex publication_date 2019/10/23 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
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 \Box(κ) implies that there is a Fréchet α1-space with Gδ-tightness equal to κ. We use the example constructed from \Box(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.