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Carnap's problem for intuitionistic propositional logic

Jul 2022

We show that intuitionistic propositional logic is \emph{Carnap categorical}:the only interpretation of the connectives consistent with the intuitionisticconsequence relation is the standard interpretation. This holds relative to themost well-known semantics with respect to which intuitionistic logic is soundand complete; among them Kripke semantics, Beth semantics, Dragalin semantics,and topological semantics. It also holds for algebraic semantics, althoughcategoricity in that case is different in kind from categoricity relative topossible worlds style semantics.

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