The existence of free ultrafilters on ω does not imply the extension of filters on ω to ultrafilters

DOI10.1002/malq.201100092zbMath1386.03063OpenAlexW1931954019MaRDI QIDQ2856631

Eric J. Hall, Eleftherios Tachtsis, Kyriakos Keremedis

Publication date: 30 October 2013

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

Full work available at URL: https://doi.org/10.1002/malq.201100092

zbMATH Keywords

compactnessfilteraxiom of choiceweak axioms of choiceBoolean prime ideal theoremfree ultrafilterstone space

Mathematics Subject Classification ID

Compactness (54D30) Consistency and independence results (03E35) Product spaces in general topology (54B10) Special constructions of topological spaces (spaces of ultrafilters, etc.) (54D80) Axiom of choice and related propositions (03E25)

Related Items (9)

ON THE SET-THEORETIC STRENGTH OF ELLIS’ THEOREM AND THE EXISTENCE OF FREE IDEMPOTENT ULTRAFILTERS ON ω ⋮ On the Existence of Free Ultrafilters on ω and on Russell-sets in ZF ⋮ Idempotent ultrafilters without Zorn’s Lemma ⋮ On a variant of Rado's selection lemma and its equivalence with the Boolean prime ideal theorem ⋮ On extensions of countable filterbases to ultrafilters and ultrafilter compactness ⋮ Hausdorff compactifications in ZF ⋮ How to have more things by forgetting how to count them ⋮ Several results on compact metrizable spaces in \(\mathbf{ZF} \) ⋮ On ultracompact spaces in ZF

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Compactness and the axiom of choice
• On the Set-Theoretic Strength of Countable Compactness of the Tychonoff Product 2^R
• Remarks on the Stone Spaces of the Integers and the Reals without AC
• Tychonoff Products of Two-Element Sets and Some Weakenings of the Boolean Prime Ideal Theorem
• On generic extensions without the axiom of choice
• The model of set theory generated by countably many generic reals
• Variants of RADO'S Selection Lemma and their Applications
• On the Compactness and Countable Compactness of 2^Rin ZF
• Axiom of choice
• The axiom of choice

This page was built for publication: The existence of free ultrafilters on ω does not imply the extension of filters on ω to ultrafilters