Cardinality without Enumeration

Studia Logica 80 (1):121-141 (2005)
  Copy   BIBTEX

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.

Other Versions

No versions found

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 103,401

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Analytics

Added to PP
2009-01-28

Downloads
84 (#257,751)

6 months
12 (#218,371)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

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.

Add more citations

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.

View all 10 references / Add more references