On the Bourbaki's fixed point theorem and the axiom of choice
Logic
2019-06-05 v2
Abstract
In this note we generalize the Moroianu's fixed point theorem. We propose a very elegant common proof of the Bourbaki's fixed point theorem and our result. We apply our result to give a very elegant proof of the fact that, in the Zermelo-Fraenkel system, the axiom of choice is equivalent to each of the following statements: H. Kneser's Lemma, Zorn's Lemma, Zermelo's Lemma
Cite
@article{arxiv.1905.09782,
title = {On the Bourbaki's fixed point theorem and the axiom of choice},
author = {Mohssin Zarouali-Darkaoui},
journal= {arXiv preprint arXiv:1905.09782},
year = {2019}
}