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An intuitionistic version of Zermelo's proof that every choice set can be well-ordered

Published online by Cambridge University Press:  12 March 2014

J. Todd Wilson
J. Todd Wilson*
Affiliation:
Department of Computer Science, California State University, Fresno, Fresno, CA 93740, E-mail: twilson@csufresno.edu
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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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 66 , Issue 3 , September 2001 , pp. 1121 - 1126
Copyright
Copyright © Association for Symbolic Logic 2001

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References

REFERENCES

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