Step by step-building representations in algebraic logic

Journal of Symbolic Logic 62 (1):225-279 (1997)
We consider the problem of finding and classifying representations in algebraic logic. This is approached by letting two players build a representation using a game. Homogeneous and universal representations are characterized according to the outcome of certain games. The Lyndon conditions defining representable relation algebras (for the finite case) and a similar schema for cylindric algebras are derived. Finite relation algebras with homogeneous representations are characterized by first order formulas. Equivalence games are defined, and are used to establish whether an algebra is ω-categorical. We have a simple proof that the perfect extension of a representable relation algebra is completely representable. An important open problem from algebraic logic is addressed by devising another two-player game, and using it to derive equational axiomatisations for the classes of all representable relation algebras and representable cylindric algebras. Other instances of this approach are looked at, and include the step by step method
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DOI 10.2307/2275740
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Completing Theories by Forcing.Jon Barwise & Abraham Robinson - 1970 - Annals of Mathematical Logic 2 (2):119-142.
Axioms for Tense Logic. I. ``Since'' and ``Until''.John P. Burgess - 1982 - Notre Dame Journal of Formal Logic 23 (4):367-374.

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Citations of this work BETA
Algebraic Logic, Where Does It Stand Today?Sayed Ahmed Tarek - 2005 - Bulletin of Symbolic Logic 11 (4):465-516.
Atom Structures of Cylindric Algebras and Relation Algebras.Ian Hodkinson - 1997 - Annals of Pure and Applied Logic 89 (2):117-148.
Relation Algebras From Cylindric Algebras, I.Robin Hirsch & Ian Hodkinson - 2001 - Annals of Pure and Applied Logic 112 (2-3):225-266.
Omitting Types for Algebraizable Extensions of First Order Logic.Sayed Ahmed Tarek - 2005 - Journal of Applied Non-Classical Logics 15 (4):465-489.

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