Journal of Symbolic Logic
- J. Symbolic Logic
- Volume 68, Issue 3 (2003), 879- 884.
Non-well-foundedness of well-orderable power sets
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|.
J. Symbolic Logic, Volume 68, Issue 3 (2003), 879- 884.
First available in Project Euclid: 17 July 2003
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Forster, T. E.; Truss, J. K. Non-well-foundedness of well-orderable power sets. J. Symbolic Logic 68 (2003), no. 3, 879-- 884. doi:10.2178/jsl/1058448446. https://projecteuclid.org/euclid.jsl/1058448446