Realizability for Peano arithmetic with winning conditions in HON games

Valentin Blot (1)

1 Department of Computer Science [Bath]

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.

Domaines: Logique en informatique [cs.LO]

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