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
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history
Request removal from index
Download options
Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 26,146
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.

Monthly downloads

Added to index

2009-01-28

Total downloads

8 ( #482,731 of 2,151,600 )

Recent downloads (6 months)

1 ( #397,093 of 2,151,600 )

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Order:
There  are no threads in this forum
Nothing in this forum yet.

Other forums