Relation algebras from cylindric algebras, I

Abstract

We characterise the class S Ra CA n of subalgebras of relation algebra reducts of n-dimensional cylindric algebras (for finite n⩾5) by the notion of a ‘hyperbasis’, analogous to the cylindric basis of Maddux, and by representations. We outline a game–theoretic approximation to the existence of a representation, and how to use it to obtain a recursive axiomatisation of S Ra CA n .