Relation algebras from cylindric algebras, I

Robin Hirsch and Ian Hodkinson

We characterise the class SRa CA_n of subalgebras of relation algebra reducts of n-dimensional cylindric algebras (for finite n, at least 4) by the notion of a hyperbasis,analogous to the cylindric basis of Maddux, and by relativised representations. A corollary is that S Ra CA_n = S Ra(CA_n \cap Crs_n)=S Ra(CA_n \cap G_n).  We give a game-theoretic approximation to the existence of a representation, and use it to obtain a recursive equational axiomatisation of S Ra CA_n.  We include notes on n-variable proof theory, homogeneity, and related matters, and some open problems.

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