Realizability for Peano Arithmetic with Winning Conditions in HON Games
- Cite this paper as:
- Blot V. (2013) Realizability for Peano Arithmetic with Winning Conditions in HON Games. In: Hasegawa M. (eds) Typed Lambda Calculi and Applications. TLCA 2013. Lecture Notes in Computer Science, vol 7941. Springer, Berlin, Heidelberg
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.
Unable to display preview. Download preview PDF.