On a Certain Notion of Finite and a Finiteness Class in Set Theory without Choice
Volume 63 / 2015
Bulletin Polish Acad. Sci. Math. 63 (2015), 89-112
MSC: Primary 03E25; Secondary 03E35.
DOI: 10.4064/ba63-2-1
Abstract
We study the deductive strength of properties under basic set-theoretical operations of the subclass $E$-$\mathbf {Fin}$ 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 $f:Y\rightarrow X$.
