 A matrix is a special kind of algebra. An algebra is a matrix without a set D of designated elements. Boolean algebras correspond to matrices for propositional logic. According to Bull and Segerberg (1984: 10) the generalization from matrices to algebras may have had the effect of encouraging the study of these structures independently of their connections to logic and modal systems. The set of designated elements D in fact facilitates a definition of validity with respect to which the theorems of a system can be evaluated. Without such a set the most obvious link to logic is severed. A second generalization to classes of algebras, rather than merely to individual algebras, was also crucial to the mathematical development of the subject matter. Tarski is the towering figure in such development.