On the minimal cover property in \(\mathbf{ZF}\)

DOI10.1016/j.topol.2014.05.021zbMath1305.03038OpenAlexW2037792067MaRDI QIDQ2250127

Eleftherios Tachtsis, Paul E. Howard

Publication date: 4 July 2014

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.topol.2014.05.021

zbMATH Keywords

Cantor cubecompactnessaxiom of choiceBoolean prime ideal theoremRado's selection lemmaminimal cover propertypermutation model

Mathematics Subject Classification ID

Compactness (54D30) Consistency and independence results (03E35) Product spaces in general topology (54B10) Axiom of choice and related propositions (03E25)

Related Items (3)

On the set-theoretic strength of the $n$-compactness of generalized Cantor cubes ⋮ On the minimal cover property and certain notions of finite ⋮ On variants of the principle of consistent choices, the minimal cover property and the 2-compactness of generalized Cantor cubes

Cites Work

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• Canonical subbase-compactness of topological products
• Some consequences of Rado's selection lemma
• Compact and Loeb Hausdorff spaces in \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathsf {ZF}$\end{document} and the axiom of choice for families of finite sets
• On the set-theoretic strength of the $n$-compactness of generalized Cantor cubes
• Tychonoff Products of Two-Element Sets and Some Weakenings of the Boolean Prime Ideal Theorem
• RADO'S SELECTION LEMMA DOES NOT IMPLY THE BOOLEAN PRIME IDEAL THEOREM
• Variants of RADO'S Selection Lemma and their Applications
• A New Proof of the Tychonoff Theorem
• Axiomatic Treatment of Rank in Infinite Sets

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