Journal of Symbolic Logic 68 (3):879-884 (2003)
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|
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The Strength of Mac Lane Set Theory.A. R. D. Mathias - 2001 - Annals of Pure and Applied Logic 110 (1-3):107-234.
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