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Relation algebras of every dimension

Published online by Cambridge University Press:  12 March 2014

Roger D. Maddux
Roger D. Maddux*
Affiliation:
Department of Mathematics, Iowa State University, Ames, Iowa 50011, E-mail: maddux@vincent.iastate.edu
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Abstract

Conjecture (1) of [Ma83] is confirmed here by the following result: if 3 ≤ α < ω, then there is a finite relation algebra of dimension α, which is not a relation algebra of dimension α + 1. A logical consequence of this theorem is that for every finite α ≥ 3 there is a formula of the form S ⊆ T (asserting that one binary relation is included in another), which is provable with α + 1 variables, but not provable with only α variables (using a special sequent calculus designed for deducing properties of binary relations).

Keywords

Logiccomplexity of proofsprovability with finitely many variablesrelation algebrasrelational basisdimension
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 57 , Issue 4 , December 1992 , pp. 1213 - 1229
Copyright
Copyright © Association for Symbolic Logic 1992

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References

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