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

Volume 63 / 2015

Horst Herrlich, Paul Howard, Eleftherios Tachtsis 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 $f:Y\rightarrow X$.

Authors

  • Horst Herrlich($\dagger $\ March 13, 2015)
  • Paul HowardDepartment of Mathematics
    Eastern Michigan University
    Ypsilanti, MI 48197, U.S.A.
    e-mail
  • Eleftherios TachtsisDepartment of Mathematics
    University of the Aegean
    Karlovassi, Samos 83200, Greece
    e-mail

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