A modal calculus analogous to k4w, based on intuitionistic propositional logic, iℴ

Studia Logica 38 (3):297 - 311 (1979)
Abstract
This paper treats a kind of a modal logic based on the intuitionistic propositional logic which arose from the provability predicate in the first order arithmetic. The semantics of this calculus is presented in both a relational and an algebraic way.Completeness theorems, existence of a characteristic model and of a characteristic frame, properties of FMP and FFP and decidability are proved.
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    M. H. Lob (1955). Solution of a Problem of Leon Henkin. Journal of Symbolic Logic 20 (2):115-118.
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