On the logical structure of some maximality and well-foundedness principles equivalent to choice principles
Logic in Computer Science
2024-05-17 v1 Logic
Abstract
We study the logical structure of Teichm{\"u}ller-Tukey lemma, a maximality principle equivalent to the axiom of choice and show that it corresponds to the generalisation to arbitrary cardinals of update induction, a well-foundedness principle from constructive mathematics classically equivalent to the axiom of dependent choice.From there, we state general forms of maximality and well-foundedness principles equivalent to the axiom of choice, including a variant of Zorn's lemma. A comparison with the general class of choice and bar induction principles given by Brede and the first author is initiated.
Cite
@article{arxiv.2405.09946,
title = {On the logical structure of some maximality and well-foundedness principles equivalent to choice principles},
author = {Hugo Herbelin},
journal= {arXiv preprint arXiv:2405.09946},
year = {2024}
}