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Journal Article

An Intuitionistic Version of Zermelo's Proof That Every Choice Set Can Be Well-Ordered

J. Todd Wilson
The Journal of Symbolic Logic
Vol. 66, No. 3 (Sep., 2001), pp. 1121-1126
DOI: 10.2307/2695096
https://www.jstor.org/stable/2695096
Page Count: 6
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An Intuitionistic Version of Zermelo's Proof That Every Choice Set Can Be Well-Ordered
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Abstract

We give a proof, valid in any elementary topos, of the theorem of Zermelo that any set possessing a choice function for its set of inhabited subsets can be well-ordered. Our proof is considerably simpler than existing proofs in the literature and moreover can be seen as a direct generalization of Zermelo's own 1908 proof of his theorem.