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Notions of compactness for special subsets of ℝ I and some weak forms of the axiom of choice

Marianne Morillon

Journal of Symbolic Logic 75 (1):255-268 (2010)

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The Compactness of 2^R and the Axiom of Choice.Kyriakos Keremedis - 2000 - Mathematical Logic Quarterly 46 (4):569-571.details We show that for every we ordered cardinal number m the Tychonoff product 2m is a compact space without the use of any choice but in Cohen's Second Mode 2ℝ is not compact. Axioms of Set Theory in Philosophy of Mathematics Direct download (2 more) Export citation Bookmark 2 citations
The Axiom of Choice.Gershon Sageev - 1976 - Journal of Symbolic Logic 41 (4):784-785.details Logic and Philosophy of Logic Direct download Export citation Bookmark 55 citations
Compactness in Countable Tychonoff Products and Choice.Paul Howard, K. Keremedis & J. E. Rubin - 2000 - Mathematical Logic Quarterly 46 (1):3-16.details We study the relationship between the countable axiom of choice and the Tychonoff product theorem for countable families of topological spaces. Axioms of Set Theory in Philosophy of Mathematics Direct download (2 more) Export citation Bookmark 5 citations
Products of compact spaces in the least permutation model.Norbert Brunner - 1985 - Mathematical Logic Quarterly 31 (25‐28):441-448.details Areas of Mathematics in Philosophy of Mathematics Direct download Export citation Bookmark 5 citations
Products of Compact Spaces in the Least Permutation Model.Norbert Brunner - 1985 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 31 (25-28):441-448.details Areas of Mathematics in Philosophy of Mathematics Direct download Export citation Bookmark 5 citations

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