Nonfinite axiomatizability results for cylindric and relation algebras

Journal of Symbolic Logic 54 (3):951-974 (1989)
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Abstract

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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10.2307/2274756

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Citations of this work

Cylindric modal logic.Yde Venema - 1995 - Journal of Symbolic Logic 60 (2):591-623.
Algebraic Logic, Where Does It Stand Today?Tarek Sayed Ahmed - 2005 - Bulletin of Symbolic Logic 11 (3):465-516.
Provability with finitely many variables.Robin Hirsch, Ian Hodkinson & Roger D. Maddux - 2002 - Bulletin of Symbolic Logic 8 (3):348-379.

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References found in this work

Cylindric Algebras.Leon Henkin & Alfred Tarski - 1967 - Journal of Symbolic Logic 32 (3):415-416.
A sequent calculus for relation algebras.Roger Maddux - 1983 - Annals of Pure and Applied Logic 25 (1):73-101.

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