Studia Logica 54 (1):61-78 (1995)
For an arbitrary similarity type of Boolean Algebras with Operators we define a class ofSahlqvist identities. Sahlqvist identities have two important properties. First, a Sahlqvist identity is valid in a complex algebra if and only if the underlying relational atom structure satisfies a first-order condition which can be effectively read off from the syntactic form of the identity. Second, and as a consequence of the first property, Sahlqvist identities arecanonical, that is, their validity is preserved under taking canonical embedding algebras. Taken together, these properties imply that results about a Sahlqvist variety V van be obtained by reasoning in the elementary class of canonical structures of algebras in V.We give an example of this strategy in the variety of Cylindric Algebras: we show that an important identity calledHenkin's equation is equivalent to a simpler identity that uses only one variable. We give a conceptually simple proof by showing that the first-order correspondents of these two equations are equivalent over the class of cylindric atom structures.
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References found in this work BETA
Varieties of Complex Algebras.Robert Goldblatt - 1989 - Annals of Pure and Applied Logic 44 (3):173-242.
Algebraization of Quantifier Logics, an Introductory Overview.István Németi - 1991 - Studia Logica 50 (3-4):485 - 569.
A New Proof of Sahlqvist's Theorem on Modal Definability and Completeness.G. Sambin & V. Vaccaro - 1989 - Journal of Symbolic Logic 54 (3):992-999.
The McKinsey Axiom is Not Canonical.Robert Goldblatt - 1991 - Journal of Symbolic Logic 56 (2):554-562.
Citations of this work BETA
Elementary Canonical Formulae: Extending Sahlqvist's Theorem.Valentin Goranko & Dimiter Vakarelov - 2006 - Annals of Pure and Applied Logic 141 (1):180-217.
Canonicity Results of Substructural and Lattice-Based Logics.Tomoyuki Suzuki - 2010 - Review of Symbolic Logic 4 (1):1-42.
A Sahlqvist Theorem for Substructural Logic.Tomoyuki Suzuki - 2013 - Review of Symbolic Logic 6 (2):229-253.
Erdős Graphs Resolve Fine's Canonicity Problem.Robert Goldblatt, Ian Hodkinson & Yde Venema - 2004 - Bulletin of Symbolic Logic 10 (2):186-208.
Notions of Density That Imply Representability in Algebraic Logic.Hajnal Andréka, Steven Givant, Szabolcs Mikulás, István Németi & András Simon - 1998 - Annals of Pure and Applied Logic 91 (2-3):93-190.
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