Relations Between Some Cardinals in the Absence of the Axiom of Choice

DOI10.2307/2687776zbMath1001.03041arXivmath/0010268OpenAlexW2134141694WikidataQ114004519 ScholiaQ114004519MaRDI QIDQ2736586

Saharon Shelah, Lorenz Halbeisen

Publication date: 10 September 2001

Published in: Bulletin of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0010268

zbMATH Keywords

surveyFraenkel-Mostowski independence proofs

Mathematics Subject Classification ID

Research exposition (monographs, survey articles) pertaining to mathematical logic and foundations (03-02) Consistency and independence results (03E35) Ordinal and cardinal numbers (03E10) Axiom of choice and related propositions (03E25)

Related Items (9)

A weird relation between two cardinals ⋮ The power set and the set of permutations with finitely many non‐fixed points of a set ⋮ FACTORIALS OF INFINITE CARDINALS IN ZF PART II: CONSISTENCY RESULTS ⋮ Generalizations of Cantor's theorem in ⋮ Factorials and the finite sequences of sets ⋮ Hierarchical multiverse of sets ⋮ Relations between cardinalities of the finite sequences and the finite subsets of a set ⋮ A note on weakly Dedekind finite sets ⋮ Four cardinals and their relations in \textsf{ZF}

Cites Work

• Set theory. An introduction to independence proofs. 2nd print
• Auswahlaxiom in der Algebra
• Verallgemeinerte Kontinuumshypothese und Auswahlaxiom
• Zur Axiomatik der Mengenlehre (Fundierungs‐ und Auswahlaxiom)
• Consequences of arithmetic for set theory
• Strongly Amorphous Sets and Dual Dedekind Infinity
• Ein Beitrag Zur Kardinalzahlarithmetik Ohne Auswahlaxiom
• The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis
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