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On a Certain Notion of Finite and a Finiteness Class in Set Theory without Choice

Herrlich H., Howard P., Tachtsis E.

Bulletin of the Polish Academy of Sciences. Mathematics

2015

Vol. 63, no. 2

89--112

We study the deductive strength of properties under basic set-theoretical operations of the subclass E-Fin of the Dedekind finite sets in set theory without the Axiom of Choice (AC), which consists of all E-finite sets, where a set X is called E-finite if for no proper subset Y of X is there a surjection f:Y→X.