Non-well-foundedness of well-orderable power sets

Journal of Symbolic Logic 68 (3):879-884 (2003)

Abstract
Tarski [5] 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|
Keywords well-orderable   well-founded   cardinal number
Categories (categorize this paper)
DOI 10.2178/jsl/1058448446
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 45,305
Through your library

References found in this work BETA

The Strength of Mac Lane Set Theory.A. R. D. Mathias - 2001 - Annals of Pure and Applied Logic 110 (1-3):107-234.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

The Dense Linear Ordering Principle.David Pincus - 1997 - Journal of Symbolic Logic 62 (2):438-456.
Monotone Reducibility and the Family of Infinite Sets.Douglas Cenzer - 1984 - Journal of Symbolic Logic 49 (3):774-782.
The Ideal of Orderable Subsets of a Set.John L. Hickman - 1978 - Notre Dame Journal of Formal Logic 19 (4):593-598.
Sets and Point-Sets: Five Grades of Set-Theoretic Involvement in Geometry.John P. Burgess - 1988 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1988:456 - 463.
Flat Sets.Arthur D. Grainger - 1994 - Journal of Symbolic Logic 59 (3):1012-1021.
Finite Mathematics.Shaughan Lavine - 1995 - Synthese 103 (3):389 - 420.

Analytics

Added to PP index
2009-01-28

Total views
10 ( #761,434 of 2,280,232 )

Recent downloads (6 months)
1 ( #830,174 of 2,280,232 )

How can I increase my downloads?

Downloads

My notes

Sign in to use this feature