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Semantics for Intuitionistic Arithmetic Based on Tarski Games with Retractable Moves

  • Stefano Berardi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4583)

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 \({\tt HA_{\mbox{\tiny inf}}}\).

Keywords

Active Move Logical Rule Conservative Extension Pointed Sequent Recursive Tree 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Stefano Berardi
    • 1
  1. 1.C.S. Dept., University of TorinoItaly

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