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A proof of zermelo's theorem

Published online by Cambridge University Press:  12 March 2014

Vladimir Dévidé
Vladimir Dévidé*
Affiliation:
University of Zagreb
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Extract

We give a short proof of the theorem that, assuming the axiom of choice, every set can be well-ordered. The proof makes direct use of neither induction nor ordinals.

Let S be any given set and its power-set. Let be a choice function, i.e. we denote Ζ — {γΖ} by Ζ'.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 32 , Issue 3 , 09 October 1967 , pp. 366
Copyright
Copyright © Association for Symbolic Logic 1967

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