 Apart from model theory, Tarski revived the algebra of relations in his 1941 paper “On the Calculus of Relations”. First he outlined a formal logic based on allowing quantification over both elements and relations, and then he turned to a more detailed study of the quantifier-free formulas of this system that involved only relation variables. After presenting a list of axioms that obviously held in the algebra of relations as presented in Schröder’s third volume he proved that these axioms allowed one to reduce quantifier-free relation formulas to equations. Thus his calculus of relations became the study of a certain equational theory which he noted had the same relation to the study of all binary relations on sets as the equational theory of Boolean algebra had to the study of all subsets of sets. This led to questions paralleling those already posed and resolved for Boolean algebras, for example, was every model of his axioms for relation algebras isomorphic to an algebra of relations on a set? One question had been answered by Arwin Korselt (1864–1947), namely there were first-order sentences in the theory of binary relations that were not equivalent to an equation in the calculus of relations—thus the calculus of relations definitely had a weaker expressive power than the first-order theory of relations. Actually the expressive power of relation algebra is exactly equivalent to first-order logic with just three variables. However, if in relation algebras (the calculus of relations) one wants to formalize a set theory which has something such as the pair axiom, then one can reduce many variables to three variables, and so it is possible to express any first-order statement of such a theory by an equation. Monk proved that, unlike the calculus of classes, there is no finite equational basis for the calculus of binary relations (see Monk 1964). Tarski and Givant (1987) showed that the equational logic of relation algebras is so expressive that one can carry out first-order set theory in it.