Abstract. This paper contributes to the investigation of general relation algebras in connection with first order definable operations: e.g. Boolean systems of relations with projections (BSP) are algebras of relations closed with respect to set-theoretical operations definable by first order formulas without equality. As in the case of relational clones and Krasner algebras, BSP are Galois closed sets with respect to a Galois connection -- the strong invariance -- between operations (here unary operations) and relations. They can internally be described also as extensions of Krasner algebras. Variations of the first order formulas under considerations lead to several Galois connections the Galois closed elements of which are also completely characterized. In a unified setting instead of unary functions we use multifunctions as objects corresponding to relations w.r.t. the Galois connection.

AMS Subject Classification (1991): 08A02, 03G99, 06A15

Keyword(s): relation algebra, Galois connection, strongly invariant relation, first order logic without equality, multifunction

Received April 3, 1998, and in revised form March 30, 2001. (Registered under 2855/2009.)