Geodesic
On a Certain Notion of Finite and a Finiteness Class in Set Theory without Choice
Horst Herrlich1 ; Paul Howard2 ; Eleftherios Tachtsis3
1($\dagger $\ March 13, 2015)
2Department of Mathematics Eastern Michigan University Ypsilanti, MI 48197, U.S.A.
3Department of Mathematics University of the Aegean Karlovassi, Samos 83200, Greece
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 63 (2015) no. 2, pp. 89-112
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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 $f:Y\rightarrow X$.
DOI : 10.4064/ba63-2-1
Keywords: study deductive strength properties under basic set theoretical operations subclass e mathbf fin dedekind finite sets set theory without axiom choice which consists e finite sets where set called e finite proper subset there surjection rightarrow

Horst Herrlich  1   ; Paul Howard  2   ; Eleftherios Tachtsis  3

1 ($\dagger $\ March 13, 2015)
2 Department of Mathematics Eastern Michigan University Ypsilanti, MI 48197, U.S.A.
3 Department of Mathematics University of the Aegean Karlovassi, Samos 83200, Greece 
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Horst Herrlich; Paul Howard; Eleftherios Tachtsis. On a Certain Notion of Finite and a Finiteness Class in Set Theory without Choice. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 63 (2015) no. 2, pp. 89-112. doi: 10.4064/ba63-2-1

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