Realizability for Peano Arithmetic with Winning Conditions in HON Games

  • Valentin Blot
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7941)


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.


Classical Logic Function Symbol Deduction System Simple Type Winning Strategy 
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© 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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