Relativized Relation Algebras
Maarten Marx

Abstract:
Abstract Relativization is one of the central topics in the study of 
algebras of relations (i.e. relation and cylindric algebras). Relativized 
representable relation algebras behave much nicer than the original class 
RRA: for instance, one obtains finite axiomatizability, decidability and 
amalgamation by relativization. The properties of the class obtained by 
relativizing RRA depend on the kind of element with which is relativized. 
We give a systematic account of all interesting choices of relativizing 
RRA, and show that relativizing with transitive elements forms the 
borderline where all above mentioned three properties switch from negative 
to positive.

To appear in `Algebra Universalis'.