Realizability for Peano Arithmetic with Winning Conditions in HON Games

Valentin Blot (1)

1 LIP - Laboratoire de l'Informatique du Parallélisme

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.

Mots clés: Classical realizability; Peano arithmetic; Hyland Ong game semantics

Domaines: Logique en informatique [cs.LO]

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-00793324v4⟩