UNIVERSAL HORN CLASSES AND ANTIVARIETIES OF ALGEBRAIC SYSTEMS

We define and study universal Horn classes dual to varieties in both the syntactic and the semantic sense. Such classes, which we call antivarieties, appear naturally, e.g.. in graph theory and in formal language theory. The basic results are the characterization theorem for antivarieties. the theorem on cores in axiomatizable color-families, and the decidability theorem for universal theories of families of interpretation of formal languages.