Connections between quasi-projective relation algebras and cylindric algebras

• Autores: András Simon
• Localización: Algebra universalis, ISSN 0002-5240, Vol. 56, Nº. 3-4, 2007, págs. 263-301
• Idioma: inglés
• DOI: 10.1007/s00012-007-1999-z
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• Resumen

  • 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.