Cardinality without Enumeration

Studia Logica 80 (1):121-141 (2005)
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Abstract

We show that the notion of cardinality of a set is independent from that of wellordering, and that reasonable total notions of cardinality exist in every model of ZF where the axiom of choice fails. Such notions are either definable in a simple and natural way, or non-definable, produced by forcing. Analogous cardinality notions exist in nonstandard models of arithmetic admitting nontrivial automorphisms. Certain motivating phenomena from quantum mechanics are also discussed in the Appendix.

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10.1007/s11225-005-6780-8

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Athanassios Tzouvaras
Aristotle University of Thessaloniki (PhD)

Citations of this work

No two entities without identity.Benjamin C. Jantzen - 2011 - Synthese 181 (3):433-450.
Many entities, no identity.Jonas R. Becker Arenhart - 2012 - Synthese 187 (2):801-812.
Ontology of Divinity.Mirosław Szatkowski (ed.) - 2024 - Boston: De Gruyter.

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References found in this work

[Omnibus Review].Thomas Jech - 1992 - Journal of Symbolic Logic 57 (1):261-262.
On a quasi-set theory.Décio Krause - 1992 - Notre Dame Journal of Formal Logic 33 (3):402--11.
Constructive set theory.John Myhill - 1975 - Journal of Symbolic Logic 40 (3):347-382.

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