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. Our winning conditions are sets of desequentialized interactions which we call positions. 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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Annals of Pure and Applied Logic, Elsevier Masson, 2017, 168 (2), pp.254 - 277. 〈10.1016/j.apal.2016.10.006〉
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Soumis le : samedi 14 avril 2018 - 14:36:21
Dernière modification le : mardi 17 avril 2018 - 14:52:38

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Valentin Blot. Realizability for Peano arithmetic with winning conditions in HON games. Annals of Pure and Applied Logic, Elsevier Masson, 2017, 168 (2), pp.254 - 277. 〈10.1016/j.apal.2016.10.006〉. 〈hal-01766884〉

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