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- W2168995070 abstract "Abstract This paper considers Henkin’s proof of completeness of classical first-order logic and extends its scope to the realm of algebraizable logics in the sense of Blok and Pigozzi. Given a propositional logic L (for which we only need to assume that it has an algebraic semantics and a suitable disjunction) we axiomatize two natural first-order extensions L∀ m and L∀ and prove that the former is complete with respect to all models over algebras from , while the latter is complete with respect to all models over relatively finitely subdirectly irreducible algebras. While the first completeness result is relatively straightforward, the second requires non-trivial modifications of Henkin’s proof by making use of the disjunction connective. As a byproduct, we also obtain a form of Skolemization provided that the algebraic semantics admits regular completions. The relatively modest assumptions on the propositional side allow for a wide generalization of previous approaches by Rasiowa, Sikorski, Hájek, Horn, and others and help to illuminate the “essentially first-order” steps in the classical Henkin’s proof." @default.
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- W2168995070 date "2015-03-01" @default.
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- W2168995070 title "A HENKIN-STYLE PROOF OF COMPLETENESS FOR FIRST-ORDER ALGEBRAIZABLE LOGICS" @default.
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- W2168995070 doi "https://doi.org/10.1017/jsl.2014.19" @default.
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