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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On comparability in a topos


Author: Radu Diaconescu
Journal: Proc. Amer. Math. Soc. 98 (1986), 389-393
MSC: Primary 18B25; Secondary 03G30, 03H15
MathSciNet review: 857927
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Abstract: While studying the category of "finite" sets associated to a nonstandard model of arithmetic [4], it became apparent that the law of trichotomy plays an important role in that context. The object of this note is to point out the strength of the obvious variants of trichotomy in a general topos. At it turns out even its mildest form (COMP) is quite restrictive, the usual variants (M-COMP, E-COMP) force the topos to be equivalent to a category of sets with AC.


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DOI: https://doi.org/10.1090/S0002-9939-1986-0857927-9
Article copyright: © Copyright 1986 American Mathematical Society