Journal of Symbolic Logic
- J. Symbolic Logic
- Volume 66, Issue 3 (2001), 1121-1126.
An Intuitionistic Version of Zermelo's Proof That Every Choice Set Can Be Well-Ordered
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.
J. Symbolic Logic, Volume 66, Issue 3 (2001), 1121-1126.
First available in Project Euclid: 6 July 2007
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Wilson, J. Todd. An Intuitionistic Version of Zermelo's Proof That Every Choice Set Can Be Well-Ordered. J. Symbolic Logic 66 (2001), no. 3, 1121--1126. https://projecteuclid.org/euclid.jsl/1183746549