Journal of Symbolic Logic 62 (1):225-279 (1997)

Abstract
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
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.2307/2275740
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 53,645
Through your library

References found in this work BETA

Model Theory.Michael Makkai, C. C. Chang & H. J. Keisler - 1991 - Journal of Symbolic Logic 56 (3):1096.
Cylindric Algebras. Part I.Leon Henkin, J. Donald Monk, Alfred Tarski, L. Henkin, J. D. Monk & A. Tarski - 1985 - Journal of Symbolic Logic 50 (1):234-237.
Cylindric Algebras. Part II.Leon Henkin, J. Donald Monk & Alfred Tarski - 1988 - Journal of Symbolic Logic 53 (2):651-653.

View all 9 references / Add more references

Citations of this work BETA

Algebraic Logic, Where Does It Stand Today?Tarek Sayed Ahmed - 2005 - Bulletin of Symbolic Logic 11 (3):465-516.
Atom Structures of Cylindric Algebras and Relation Algebras.Ian Hodkinson - 1997 - Annals of Pure and Applied Logic 89 (2):117-148.
A Modeltheoretic Solution to a Problem of Tarski.Tarek Sayed Ahmed - 2002 - Mathematical Logic Quarterly 48 (3):343-355.
Relation Algebras From Cylindric Algebras, I.Robin Hirsch & Ian Hodkinson - 2001 - Annals of Pure and Applied Logic 112 (2-3):225-266.

View all 6 citations / Add more citations

Similar books and articles

Analytics

Added to PP index
2009-01-28

Total views
177 ( #50,605 of 2,349,060 )

Recent downloads (6 months)
3 ( #238,484 of 2,349,060 )

How can I increase my downloads?

Downloads

My notes