Realizability for Peano Arithmetic with Winning Conditions in HON Games

  • Valentin Blot
Conference paper

DOI: 10.1007/978-3-642-38946-7_8

Part of the Lecture Notes in Computer Science book series (LNCS, volume 7941)
Cite this paper as:
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

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Valentin Blot
    • 1
  1. 1.Laboratoire de l’Informatique et du ParallélismeENS Lyon - Université de Lyon UMR 5668 CNRS ENS-Lyon UCBL INRIALyon cedex 07France

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