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ON THE AXIOM OF CHOICE IN A WELL-POINTED TOPOS

IG SUNG KIM

Abstract

Topos is a set-like category. For an axiom of choice in a topos, F. W. Lawvere and A. M. Penk introduced another versions of the axiom of choice. Also it is showed that general axiom of choice and Penk`s axiom of choice are weaker than Lawvere`s axiom of choice. In this paper we study that weak form of axiom of choice, axiom of choice, Penk`s axiom of choice and Lawvere`s axiom of choice are all equivalent in a well pointed topos.

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Key concepts: Axiom of choice, Urelement, Zermelo–Fraenkel set theory, Constructive set theory, Axiom independence, Mathematics, Axiom, Choice function