PFA and \(\omega_1\)-free compact spaces

DOI10.1007/s10474-021-01197-9zbMath1499.54116arXiv2104.13698OpenAlexW4206996851MaRDI QIDQ2116370

Alan Dow, Klaas Pieter Hart

Publication date: 16 March 2022

Published in: Acta Mathematica Hungarica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2104.13698

zbMATH Keywords

convergencecompactPFAfirst-countable\(\omega_1\)-sequence

Mathematics Subject Classification ID

Compactness (54D30) Noncompact covering properties (paracompact, Lindelöf, etc.) (54D20) Consistency and independence results (03E35) Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.) (54A20) Continuum hypothesis and Martin's axiom (03E50) Consistency and independence results in general topology (54A35) Generic absoluteness and forcing axioms (03E57)

Cites Work

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• Martin's axiom and separated mad families
• Generalized side-conditions and Moore-Mrówka
• A first countable, initially \(\omega _1\)-compact but non-compact space
• Set theory. An introduction to independence proofs
• Convergent Free Sequences in Compact Spaces
• On Compact Hausdorff Spaces of Countable Tightness
• Analytic quotients: theory of liftings for quotients over analytic ideals on the integers
• Reflecting Lindelöf and converging ω₁-sequences

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