1995/04/18 by Martin Goldstern, Goldstern, Martin
Mathematics · Computer Science · #Advanced Topology and Set Theory #Advanced Algebra and Logic #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.math/9504201
We give a simple example of a set that is weakly Dedekind infinite (= can be mapped onto omega) but dually Dedekind finite (=cannot be mapped noninjectively onto itself), namely, the power set of a superamorphous set. (A infinite set is superamorphous if all finitary relations on it are definable in the language of equality.) We also show that the property of "inexhaustibility" is not closed under supersets unless the full axiom of choice holds.