Non-well-foundedness of well-orderable power sets
Forster, T. E. ; Truss, J. K.
J. Symbolic Logic, Tome 68 (2003) no. 1, p. 879- 884 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
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|.
Publié le : 2003-09-14
Classification:  well-orderable,  well-founded,  cardinal number,  03E25,  03E10 
@article{1058448446,
     author = {Forster, T. E. and Truss, J. K.},
     title = {Non-well-foundedness of well-orderable power sets},
     journal = {J. Symbolic Logic},
     volume = {68},
     number = {1},
     year = {2003},
     pages = { 879- 884},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1058448446}
}

Forster, T. E.; Truss, J. K. Non-well-foundedness of well-orderable power sets. J. Symbolic Logic, Tome 68 (2003) no. 1, pp.  879- 884. http://gdmltest.u-ga.fr/item/1058448446/