Non-well-foundedness of well-orderable power sets

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

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Exclusion Principles as Restricted Permutation Symmetries.S. Tarzi - 2003 - Foundations of Physics 33 (6):955-979.

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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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