On a variant of Rado's selection lemma and its equivalence with the Boolean prime ideal theorem

DOI10.1007/s00153-014-0390-yzbMath1339.03037OpenAlexW2040734568WikidataQ124813540 ScholiaQ124813540MaRDI QIDQ481869

Eleftherios Tachtsis, Paul E. Howard

Publication date: 15 December 2014

Published in: Archive for Mathematical Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00153-014-0390-y

zbMATH Keywords

compactnessaxiom of choiceBoolean prime ideal theoremFraenkel-Mostowski permutation models of ZFAgeneralized Cantor cubesRado's selection lemma

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 (1)

On the set-theoretic strength of the $n$-compactness of generalized Cantor cubes

Cites Work

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• Some consequences of Rado's selection lemma
• The existence of free ultrafilters on ω does not imply the extension of filters on ω to ultrafilters
• 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
• On Theorems of Tychonoff, Alexander, and R. Rado
• A General Selection Principle, with Applications in Analysis and Algebra
• Axiomatic Treatment of Rank in Infinite Sets
• Choice functions and Tychonoff’s theorem
• The axiom of choice

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