Provability interpretations of modal logic
- Robert M. Solovay
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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.
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- Provability interpretations of modal logic
Israel Journal of Mathematics
Volume 25, Issue 3-4 , pp 287-304
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- 1. IBM Thomas J. Watson Research Center, 10598, Yorktown Heights, New York, USA