Universal classes of simple relation algebras

Publisher: Cambridge University Press

E-ISSN: 1943-5886|64|2|575-589

ISSN: 0022-4812

Source: The Journal of Symbolic Logic, Vol.64, Iss.2, 1999-06, pp. : 575-589

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

Previous Menu Next

Abstract

Tarski [19] proved the important theorem that the class of representable relation algebras is equationally axiomatizable. One of the key steps in his proof is showing that the class of (isomorphs of) simple set relation algebras—that is, algebras of binary relations with a unit of the form U × U for some non-empty set U —is universal, i.e., is axiomatizable by a set of universal sentences. In the same paper Tarski observed that the class of (isomorphs of) relation algebras constructed from groups (so-called group relation algebras) is also universal.