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Injective power objects and the axiom of choice. (English) Zbl 1208.03059
The author investigates the axiom of choice in a topos by interpreting the crucial term “non-empty” as being “injective”. He shows among other things that if the axiom of choice holds in the category of sets, then it holds in a wide variety of topoi, including all localic topoi, and that the topos-version has several of the classical consequences of the axiom of choice.

03G30 Categorical logic, topoi
03E25 Axiom of choice and related propositions
18B25 Topoi
Full Text: DOI
[1] Diaconescu, R., Axiom of choice and complementation, Proc. AMS, 51, 1, 176-178, (1975) · Zbl 0317.02077
[2] Freyd, P., Choice and well-ordering, Ann. pure appl. logic, 35, 149-166, (1987) · Zbl 0625.03046
[3] Freyd, P.J., Numerology in topoi, Th. app. cat., 16, 522-528, (2006) · Zbl 1103.18002
[4] Johnstone, P.T., ()
[5] Kenney, T., Copower objects & their application to finiteness in topoi, Th. app. cat., 16, 923-956, (2006) · Zbl 1113.18002
[6] Kenney, T., Generating families in a topos, Th. app. cat., 16, 896-922, (2006) · Zbl 1143.18006
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