On comparability in a topos
Proc. Amer. Math. Soc. 98 (1986), 389-393
Primary 18B25; Secondary 03G30, 03H15
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Abstract: While studying the category of "finite" sets associated to a nonstandard model of arithmetic , 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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- H. Rubin and J. E Rubin, Equivalents of the axiom of choice, North-Holland, 1963. MR 0153590 (27:3553)
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