Realizability for Peano Arithmetic with Winning Conditions in HON Games - Archive ouverte HAL
Communication Dans Un Congrès Lecture Notes in Computer Science Année : 2013

Realizability for Peano Arithmetic with Winning Conditions in HON Games

Valentin Blot
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Résumé

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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Dates et versions

hal-00793324 , version 1 (22-02-2013)
hal-00793324 , version 2 (25-02-2013)
hal-00793324 , version 3 (11-04-2013)
hal-00793324 , version 4 (05-12-2014)

Identifiants

Citer

Valentin Blot. Realizability for Peano Arithmetic with Winning Conditions in HON Games. Typed Lambda Calculi and Applications, Jun 2013, Eindhoven, Netherlands. pp 77-92, ⟨10.1007/978-3-642-38946-7_8⟩. ⟨hal-00793324v3⟩
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