On Stone’s theorem and the Axiom of Choice

DOI10.1090/S0002-9939-98-04163-XzbMath0893.54016OpenAlexW1495884122WikidataQ114009903 ScholiaQ114009903MaRDI QIDQ4383114

Chris Good, W. Stephen Watson, Ian J. Tree

Publication date: 24 March 1998

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-98-04163-x

zbMATH Keywords

axiom of choiceStone theorem

Mathematics Subject Classification ID

Noncompact covering properties (paracompact, Lindelöf, etc.) (54D20) Axiom of choice and related propositions (03E25)

Related Items (9)

Weak axioms of choice for metric spaces ⋮ Some versions of second countability of metric spaces in ZF and their role to compactness ⋮ Cuf products and cuf sums of (quasi-) metrizable spaces in ZF ⋮ On pseudocompactness and light compactness of metric spaces in $\mathbf {ZF}$ ⋮ The independence of Stone’s Theorem from the Boolean Prime Ideal Theorem ⋮ Reverse mathematics of topology: dimension, paracompactness, and splittings ⋮ Several results on compact metrizable spaces in \(\mathbf{ZF} \) ⋮ Denumerable cellular families in \(\mathbf{ZF}\) ⋮ Countable compact Hausdorff spaces need not be metrizable in ZF

Cites Work

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• Set theory. An introduction to independence proofs
• Continuing horrors of topology without choice
• Une généralisation des espaces compacts
• On a problem of W. Kinna and K. Wagner
• RADO'S SELECTION LEMMA DOES NOT IMPLY THE BOOLEAN PRIME IDEAL THEOREM
• Horrors of Topology Without AC: A Nonnormal Orderable Space
• A New Proof that Metric Spaces are Paracompact
• Paracompactness and product spaces
• The axiom of choice

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