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Computer Science > Logic in Computer Science

arXiv:2405.09946 (cs)
[Submitted on 16 May 2024]

Title:On the logical structure of some maximality and well-foundedness principles equivalent to choice principles

Authors:Hugo Herbelin (PICUBE, IRIF)
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Abstract:We study the logical structure of Teichm{ü}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 this http URL 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.
Subjects: Logic in Computer Science (cs.LO); Logic (math.LO)
Cite as: arXiv:2405.09946 [cs.LO]
  (or arXiv:2405.09946v1 [cs.LO] for this version)
  https://doi.org/10.48550/arXiv.2405.09946

Submission history

From: Hugo Herbelin [view email] [via CCSD proxy]
[v1] Thu, 16 May 2024 09:51:41 UTC (142 KB)
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