Studia Logica 54 (1):61 - 78 (1995)

Authors
Yde Venema
University of Amsterdam
Abstract
For an arbitrary similarity type of Boolean Algebras with Operators we define a class of Sahlqvist 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 are canonical, 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 called Henkin's equation is equivalent to a simpler identity that uses only one variable. We give a conceptually simple proof by showing that the firstorder correspondents of these two equations are equivalent over the class of cylindric atom structures.
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DOI 10.1007/BF01058532
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References found in this work BETA

Collected Papers.Colin McGinn - 1988 - Philosophical Review 97 (2):278.
Varieties of Complex Algebras.Robert Goldblatt - 1989 - Annals of Pure and Applied Logic 44 (3):173-242.
On the Canonicity of Sahlqvist Identities.Bjarni Jónsson - 1994 - Studia Logica 53 (4):473 - 491.

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Citations of this work BETA

A Sahlqvist Theorem for Substructural Logic.Tomoyuki Suzuki - 2013 - Review of Symbolic Logic 6 (2):229-253.
Elementary Canonical Formulae: A Survey on Syntactic, Algorithmic, and Modeltheoretic Aspects.W. Conradie, V. Goranko & D. Vakarelov - 2005 - In Renate Schmidt, Ian Pratt-Hartmann, Mark Reynolds & Heinrich Wansing (eds.), Advances in Modal Logic, Volume 5. Kings College London Publ.. pp. 17-51.

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Cylindric Algebras.Leon Henkin - 1971 - Amsterdam: North-Holland Pub. Co..
Cylindric Modal Logic.Yde Venema - 1995 - Journal of Symbolic Logic 60 (2):591-623.
Atomless Varieties.Yde Venema - 2003 - Journal of Symbolic Logic 68 (2):607-614.

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