Categorical Abstract Algebraic Logic: Wojcicki's Conjecture and Malinowski's Theorem
Categorical Abstract Algebraic Logic: Wojcicki's Conjecture and Malinowski's Theorem

Summary/Abstract: During the Autumn School on Strongly Finite Sentential Calculi held in Miedzygorze in 1977, Wojcicki conjectured that a propositional logic has a strongly adequate matrix semantics consisting of matrices with a singleton designated filter, which we call a Rasiowa semantics since it is possessed by all implicative logics of Rasiowa, if and only if it satises a simple technical condition that we name the Wojcicki condition. Malinowski proved the conjecture in 1978. We revisit Malinowski's Theorem in the setting of logics formalized as -institutions.

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