Abstract
It is well known that the model categories of universal Horn theories are locally presentable, hence essentially algebraic (see [2]). In the special case of quasivarieties a direct translation of the implicational syntax into the essentially equational one is known (see [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.
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