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Preserving cardinals and weak forms of Zorn’s lemma in realizability models

Published online by Cambridge University Press:  10 February 2021

Laura Fontanella Open the ORCID record for Laura Fontanella [Opens in a new window]  and
Guillaume Geoffroy
Laura Fontanella*
Affiliation:
Institut de Mathématiques de Marseille, Aix-Marseille Université, 163 Av. de Luminy, 13009Marseille, France
Guillaume Geoffroy
Affiliation:
Institut de Mathématiques de Marseille, Aix-Marseille Université, 163 Av. de Luminy, 13009Marseille, France
*
*Corresponding author. Email: laura.fontanella@gmail.com
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Abstract

We develop a technique for representing and preserving cardinals in realizability models, and we apply this technique to define a realizability model of Zorn’s lemma restricted to an ordinal.

Keywords

Classical realizabilityset theoryaxiom of choice
Type
Paper
Information
Mathematical Structures in Computer Science , Volume 30 , Issue 9 , October 2020 , pp. 976 - 996
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

Geoffroy, G. (2018). Réalisabilité classique: nouveaux outils et applications. Phd thesis.Google Scholar
Jech, T. J. (2003). Set Theory: The Third Millennium Edition, Berlin, Springer.Google Scholar
Jech, T. J. (1973). The Axiom of Choice, North-Holland, Amsterdam.Google Scholar
Krivine, J.-L. (2011). Realizability algebras: a program to well order R. Logical Methods in Computer Science 7 (3:02) 1–47.CrossRefGoogle Scholar
Krivine, J.-L. (2012). Realizability algebras II: new models of ZF + DC. Logical Methods in Computer Science 8 (1:10) 1–28.CrossRefGoogle Scholar
Krivine, J.-L. (2015). On the structure of classical realizability models of ZF. In: Proceedings of TYPES-2014 - LIPIcs, vol. 39, 146–161.Google Scholar
Krivine, J.-L. (2018). Realizability algebras III: some examples. Mathematical Structures in Computer Science 28 (1) 45–76.CrossRefGoogle Scholar
Kunen, K. (1980). Set theory: An Introduction to Independence Proofs, North-Holland, Amsterdam.Google Scholar
Rubin, H. and Rubin, J. E. (1985). Equivalents of the Axiom of Choice II, North-Holland, Amsterdam.Google Scholar
Sørensen, M. H. B. and Urzyczyn, P. (2006). Lectures on the Curry-Howard Isomorphism, 1st edn., vol. 149, Amsterdam, Elsevier Science.Google Scholar