ABSTRACT
Our motivation for defining terms and polynomials was to use them to define equations and identities. An equation is a statement of the form ti z
-,' t27 where t1 and t2 are terms. We will define what it means for such an equation to be satisfied, or to be an identity, in an algebra A. The relation of satisfaction, of an equation by an algebra, will give us a Galois-connection between sets of equations and classes of algebras, and allow us to consider classes of algebras which are defined by sets of equations. Finally, we show that such equational classes, or model classes, are precisely the same classes of algebras as those we are interested in from the algebraic approach of the first four chapters.
