Realizability for Peano Arithmetic with Winning Conditions in HON Games

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 Π 0 2 -formulas.
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Communication dans un congrès
Research Institute for Mathematical Sciences, Kyoto University. Typed Lambda Calculi and Applications, Jun 2013, Eindhoven, Netherlands. Springer Berlin Heidelberg, 7941, pp.77 - 92, 2013, Lecture Notes in Computer Science. <10.1007/978-3-642-38946-7_8>
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Contributeur : Valentin Blot <>
Soumis le : vendredi 5 décembre 2014 - 17:06:23
Dernière modification le : mardi 9 décembre 2014 - 01:03:57
Document(s) archivé(s) le : samedi 15 avril 2017 - 04:06:18

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Valentin Blot. Realizability for Peano Arithmetic with Winning Conditions in HON Games. Research Institute for Mathematical Sciences, Kyoto University. Typed Lambda Calculi and Applications, Jun 2013, Eindhoven, Netherlands. Springer Berlin Heidelberg, 7941, pp.77 - 92, 2013, Lecture Notes in Computer Science. <10.1007/978-3-642-38946-7_8>. <hal-00793324v4>

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