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September 2003 Non-well-foundedness of well-orderable power sets
T. E. Forster, J. K. Truss
J. Symbolic Logic 68(3): 879-884 (September 2003). DOI: 10.2178/jsl/1058448446

Abstract

Tarski [Tarski] showed that for any set X, its set w(X) of well-orderable subsets has cardinality strictly greater than that of X, even in the absence of the axiom of choice. We construct a Fraenkel-Mostowski model in which there is an infinite strictly descending sequence under the relation |w(X)| = |Y|. This contrasts with the corresponding situation for power sets, where use of Hartogs’ ℵ-function easily establishes that there can be no infinite descending sequence under the relation |𝒫(X)| = |Y|.

Citation

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T. E. Forster. J. K. Truss. "Non-well-foundedness of well-orderable power sets." J. Symbolic Logic 68 (3) 879 - 884, September 2003. https://doi.org/10.2178/jsl/1058448446

Information

Published: September 2003
First available in Project Euclid: 17 July 2003

zbMATH: 1055.03029
MathSciNet: MR2004E:03083
Digital Object Identifier: 10.2178/jsl/1058448446

Subjects:
Primary: 03E10 , 03E25

Keywords: cardinal number , well-founded , well-orderable

Rights: Copyright © 2003 Association for Symbolic Logic

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Vol.68 • No. 3 • September 2003
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