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Israel Journal of Mathematics

, Volume 25, Issue 3–4, pp 287–304 | Cite as

Provability interpretations of modal logic

  • Robert M. Solovay
Article

Abstract

We consider interpretations of modal logic in Peano arithmetic (P) determined by an assignment of a sentencev * ofP to each propositional variablev. We put (⊥)*=“0 = 1”, (χ → ψ)* = “χ* → ψ*” and let (□ψ)* be a formalization of “ψ)* is a theorem ofP”. We say that a modal formula, χ, isvalid if ψ* is a theorem ofP in each such interpretation. We provide an axiomitization of the class of valid formulae and prove that this class is recursive.

Keywords

Modal Logic Binary Relation Propositional Variable Truth Assignment Kripke Model 
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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    George Boolos,Friedman’s 35th problem has an affirmative solution, Abstract*75T-E66, Notices Amer. Math. Soc.22 (1975), A-646.Google Scholar
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Copyright information

© Hebrew University 1976

Authors and Affiliations

  • Robert M. Solovay
    • 1
  1. 1.IBM Thomas J. Watson Research CenterYorktown HeightsUSA

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