The Essentially Equational Theory of Horn Classes

It is well known that the model categories of universal Horn theories are locally presentable, hence essentially algebraic [2]. In the special case of quasivarieties a direct translation of the implicational syntax into the essentially equational one is known [1]. Here we present a similar translation for the general case, showing at the same time that many relationally presented Horn classes are in fact (equivalent to) quasivarieties. Mathematics Subject Classification (1991). Primary 03C07, Secondary 08C15.