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)
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
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 63 (2015) no. 2, pp. 89-112 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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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     title = {On a {Certain} {Notion} of {Finite} and a {Finiteness} {Class} in {Set} {Theory} without {Choice}},
     journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
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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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