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DOI: 10.4230/LIPIcs.FSCD.2024.26

On the Logical Structure of Some Maximality and Well-Foundedness Principles Equivalent to Choice Principles

Authors: Hugo Herbelin and Jad Koleilat

Published in: LIPIcs, Volume 299, 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)

Abstract

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.

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Hugo Herbelin and Jad Koleilat. On the Logical Structure of Some Maximality and Well-Foundedness Principles Equivalent to Choice Principles. In 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 299, pp. 26:1-26:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{herbelin_et_al:LIPIcs.FSCD.2024.26,
  author =	{Herbelin, Hugo and Koleilat, Jad},
  title =	{{On the Logical Structure of Some Maximality and Well-Foundedness Principles Equivalent to Choice Principles}},
  booktitle =	{9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)},
  pages =	{26:1--26:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-323-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{299},
  editor =	{Rehof, Jakob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2024.26},
  URN =		{urn:nbn:de:0030-drops-203551},
  doi =		{10.4230/LIPIcs.FSCD.2024.26},
  annote =	{Keywords: axiom of choice, Teichm\"{u}ller-Tukey lemma, update induction, constructive reverse mathematics}
}

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On the Logical Structure of Some Maximality and Well-Foundedness Principles Equivalent to Choice Principles

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