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)


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


Active Move Logical Rule Conservative Extension Pointed Sequent Recursive Tree 
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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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