Remarks on the Stone Spaces of the Integers and the Reals without AC

DOI10.4064/ba59-2-1zbMath1242.03072OpenAlexW1970625414MaRDI QIDQ3100950

Eleftherios Tachtsis, Kyriakos Keremedis, Horst Herrlich

Publication date: 22 November 2011

Published in: Bulletin of the Polish Academy of Sciences Mathematics (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/0a07b313c2d974483025d6cfd0b4acc00746b495

zbMATH Keywords

compactnessaxiom of choicefiltersultrafiltersBoolean prime ideal theoremStone spacesLoeb spacesweak forms of AC

Mathematics Subject Classification ID

Compactness (54D30) Product spaces in general topology (54B10) Stone spaces (Boolean spaces) and related structures (06E15) Special constructions of topological spaces (spaces of ultrafilters, etc.) (54D80) Axiom of choice and related propositions (03E25)

Related Items (6)

ON THE SET-THEORETIC STRENGTH OF ELLIS’ THEOREM AND THE EXISTENCE OF FREE IDEMPOTENT ULTRAFILTERS ON ω ⋮ Idempotent ultrafilters without Zorn’s Lemma ⋮ On Hausdorff operators in ZF$\mathsf {ZF}$ ⋮ On extensions of countable filterbases to ultrafilters and ultrafilter compactness ⋮ On ultracompact spaces in ZF ⋮ The existence of free ultrafilters on ω does not imply the extension of filters on ω to ultrafilters

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