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Realizability for Peano Arithmetic with Winning Conditions in HON Games

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Typed Lambda Calculi and Applications (TLCA 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7941))

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Abstract

We build a realizability model for Peano arithmetic based on winning conditions for HON games. First we define a notion of winning strategies on arenas equipped with winning conditions. We prove that the interpretation of a classical proof of a formula is a winning strategy on the arena with winning condition corresponding to the formula. Finally we apply this to Peano arithmetic with relativized quantifications and give the example of witness extraction for \(\Pi^0_2\)-formulas.

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Authors and Affiliations

  1. Laboratoire de l’Informatique et du Parallélisme, ENS Lyon - Université de Lyon UMR 5668 CNRS ENS-Lyon UCBL INRIA, 46, allée d’Italie, 69364, Lyon cedex 07, France

    Valentin Blot

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  1. Valentin Blot
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Editors and Affiliations

  1. Research Institute for Mathematical Sciences, Kyoto University, Kitashirakawa-Oiwake-cho, Sakyo-ku, 606-8502, Kyoto, Kyoto, Japan

    Masahito Hasegawa

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Blot, V. (2013). Realizability for Peano Arithmetic with Winning Conditions in HON Games. In: Hasegawa, M. (eds) Typed Lambda Calculi and Applications. TLCA 2013. Lecture Notes in Computer Science, vol 7941. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38946-7_8

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  • DOI: https://doi.org/10.1007/978-3-642-38946-7_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38945-0

  • Online ISBN: 978-3-642-38946-7

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