Journal of Symbolic Logic 68 (3):879-884 (2003)
|Abstract||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||
|Keywords||well-orderable well-founded cardinal number|
|Categories||categorize this paper)|
|Through your library||Configure|
Similar books and articles
David Pincus (1997). The Dense Linear Ordering Principle. Journal of Symbolic Logic 62 (2):438-456.
Shaughan Lavine (1995). Finite Mathematics. Synthese 103 (3):389 - 420.
Arthur D. Grainger (1994). Flat Sets. Journal of Symbolic Logic 59 (3):1012-1021.
John P. Burgess (1988). Sets and Point-Sets: Five Grades of Set-Theoretic Involvement in Geometry. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1988:456 - 463.
John L. Hickman (1978). The Ideal of Orderable Subsets of a Set. Notre Dame Journal of Formal Logic 19 (4):593-598.
Vladimir Kanovei & Michael Reeken (1996). Internal Approach to External Sets and Universes. Studia Logica 56 (3):293 - 322.
Vladimir Kanovei & Michael Reeken (1998). Elementary Extensions of External Classes in a Nonstandard Universe. Studia Logica 60 (2):253-273.
Douglas Cenzer (1984). Monotone Reducibility and the Family of Infinite Sets. Journal of Symbolic Logic 49 (3):774-782.
Paul E. Howard (1973). Limitations on the Fraenkel-Mostowski Method of Independence Proofs. Journal of Symbolic Logic 38 (3):416-422.
Paul Howard & Jean E. Rubin (1995). The Axiom of Choice for Well-Ordered Families and for Families of Well- Orderable Sets. Journal of Symbolic Logic 60 (4):1115-1117.
Added to index2009-01-28
Total downloads2 ( #246,081 of 722,856 )
Recent downloads (6 months)1 ( #60,917 of 722,856 )
How can I increase my downloads?