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Tychonoff products of compact spaces in ZF and closed ultrafilters

Kyriakos Keremedis

Mathematical Logic Quarterly 56 (5):474-487 (2010)

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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
The axiom of choice holds iff maximal closed filters exist.Horst Herrlich - 2003 - Mathematical Logic Quarterly 49 (3):323.details It is shown that in ZF set theory the axiom of choice holds iff every non empty topological space has a maximal closed filter. Axioms of Set Theory in Philosophy of Mathematics Direct download (2 more) Export citation Bookmark 1 citation
Products of Compact Spaces and the Axiom of Choice.O. De la Cruz, Paul Howard & E. Hall - 2002 - Mathematical Logic Quarterly 48 (4):508-516.details We study the Tychonoff Compactness Theorem for several different definitions of a compact space. Axioms of Set Theory in Philosophy of Mathematics Direct download Export citation Bookmark 2 citations
Consequences of the Axiom of Choice.Paul Howard & Jean E. Rubin - 2005 - Bulletin of Symbolic Logic 11 (1):61-63.details Axioms of Set Theory in Philosophy of Mathematics Logic and Philosophy of Logic Export citation Bookmark 21 citations

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