Semantics for intuitionistic arithmetic based on Tarski games with retractable moves

Authors:
Stefano Berardi
Affiliations:
C.S. Dept., University of Torino, Italy
Venue:
TLCA'07 Proceedings of the 8th international conference on Typed lambda calculi and applications
Year:
2007

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Abstract

We define an effective, sound and complete game semantics for HAinf, Intuitionistic Arithmetic with ω-rule. Our semantics is equivalent to the original semantics proposed by Lorentzen [6], but it is based on the more recent notions of "backtracking" ([5], [2]) and of isomorphism between proofs and strategies ([8]). We prove that winning strategies in our game semantics are tree-isomorphic to the set of proofs of some variant of HAinf, and that they are a sound and complete interpretation of HAinf.