Relation Algebras from Cylindric Algebras, I

We characterise the class SRaCA n of subalgebras of relation algebra reducts of n-dimensional cylindric algebras (for nite n 5) by the notion of a `hyper-basis', analogous to the cylindric basis of Maddux, and by relativised representations. A corollary is that SRaCA n = SRa(CA n \ Crs n) = SRa(CA n \ G n). We outline a game-theoretic approximation to the existence of a representation, and how to use it to obtain a recursive axiomatisation of SRaCA n .