Resumen de Connections between quasi-projective relation algebras and cylindric algebras

András Simon

• In this paper we show that every quasi-projective relation algebra (QRA) has within it cylindric algebras (CAs) of all finite dimensions greater than two such that (i) they are term-definable in the QRA, (ii) they have a relation algebraic reduct that is isomorphic to the QRA and (iii) these isomorphisms are also term-definable. Furthermore, these CAs form a sequence such that each of them is isomorphic to a neat reduct of the higher dimensional ones, and these isomorphisms are also term-definable. These observations yield a new proof of the representation theorem of QRAs, due to Tarski, that is fundamentally different from both his original proof and Maddux's, who generalized Tarski's theorem to a much wider class of algebras.