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Another equivalent form of the axiom of choice

1966
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Proceedings of the American Mathematical Society
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It seems to be generally accepted that work in the theory of categories requires the strong axiom of choice which says that the class of all sets can be well-ordered, or that there is a class which is a singlevalued choice function whose domain is the class of all nonempty sets. This note points out the Theorem. If every category has a skeleton, then the strong axiom of choice holds. Proof. Define a category e whose objects are all pairs (X, x) consisting of a set X and a distinguished element

doi:10.1090/s0002-9939-1966-0186535-8
fatcat:dyn336jq7nag7lxxu5fjasjgky