On the logical structure of some maximality and well-foundedness principles equivalent to choice principles
<|reference_start|>On the logical structure of some maximality and well-foundedness principles equivalent to choice principles: 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.<|reference_end|>
@article{herbelin2024on,
    title={On the logical structure of some maximality and well-foundedness
  principles equivalent to choice principles},
    author={Hugo Herbelin (PICUBE, IRIF)},
    journal={arXiv preprint arXiv:2405.09946},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.09946},
    primaryClass={cs.LO math.LO}
}