Abstract
We define an effective, sound and complete game semantics for \({\tt HA_{\mbox{\tiny inf}}}\), 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 \({\tt HA_{\mbox{\tiny inf}}}\), and that they are a sound and complete interpretation of \({\tt HA_{\mbox{\tiny inf}}}\).
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References
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Berardi, S. (2007). Semantics for Intuitionistic Arithmetic Based on Tarski Games with Retractable Moves. In: Della Rocca, S.R. (eds) Typed Lambda Calculi and Applications. TLCA 2007. Lecture Notes in Computer Science, vol 4583. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73228-0_4
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DOI: https://doi.org/10.1007/978-3-540-73228-0_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73227-3
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