Journal of Symbolic Logic

Nonfinite Axiomatizability Results for Cylindric and Relation Algebras

Roger D. Maddux

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The set of equations which use only one variable and hold in all representable relation algebras cannot be derived from any finite set of equations true in all representable relation algebras. Similar results hold for cylindric algebras and for logic with finitely many variables. The main tools are a construction of nonrepresentable one-generated relation algebras, a method for obtaining cylindric algebras from relation algebras, and the use of relation algebras in defining algebraic semantics for first-order logic.

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J. Symbolic Logic, Volume 54, Issue 3 (1989), 951-974.

First available in Project Euclid: 6 July 2007

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Maddux, Roger D. Nonfinite Axiomatizability Results for Cylindric and Relation Algebras. J. Symbolic Logic 54 (1989), no. 3, 951--974.

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