Relations between some cardinals in the absence of the axiom of choice

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Bulletin of Symbolic Logic 7 (2):237-261 (2001)
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Abstract

If we assume the axiom of choice, then every two cardinal numbers are comparable, In the absence of the axiom of choice, this is no longer so. For a few cardinalities related to an arbitrary infinite set, we will give all the possible relationships between them, where possible means that the relationship is consistent with the axioms of set theory. Further we investigate the relationships between some other cardinal numbers in specific permutation models and give some results provable without using the axiom of choice

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10.2307/2687776

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Citations of this work

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Factorials and the finite sequences of sets.Nattapon Sonpanow & Pimpen Vejjajiva - 2019 - Mathematical Logic Quarterly 65 (1):116-120.
A weird relation between two cardinals.Lorenz Halbeisen - 2018 - Archive for Mathematical Logic 57 (5-6):593-599.

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References found in this work

Set theory and the continuum hypothesis.Paul J. Cohen - 1966 - New York,: W. A. Benjamin.
[Omnibus Review].Thomas Jech - 1992 - Journal of Symbolic Logic 57 (1):261-262.
Zur Axiomatik der Mengenlehre (Fundierungs‐ und Auswahlaxiom).Ernst Specker - 1957 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 3 (13‐20):173-210.
Consequences of arithmetic for set theory.Lorenz Halbeisen & Saharon Shelah - 1994 - Journal of Symbolic Logic 59 (1):30-40.

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