2026-09-22T03:57:35Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:20355 2026-09-05T16:41:48Z ddc:004 open_access

On the Logical Structure of Some Maximality and Well-Foundedness Principles Equivalent to Choice Principles Herbelin, Hugo Koleilat, Jad axiom of choice Teichmüller-Tukey lemma update induction constructive reverse mathematics We study the logical structure of Teichmüller-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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Hugo Herbelin and Jad Koleilat 2024 Is Part Of LIPIcs, Volume 299, 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.FSCD.2024.26 urn:nbn:de:0030-drops-203551 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2024.26 eng https://creativecommons.org/licenses/by/4.0/legalcode