Categorical Horn classes. II (Q541986)

A class of structures is called a Horn class if it is axiomatizable and closed under taking reduced products. The paper under review is a continuation of Part I, published a long time ago [Algebra Logic 19, 377--400 (1981); translation from Algebra Logika 19, 582--614 (1980; Zbl 0491.03011)]. A characterization of uncountably categorical Horn classes is obtained which implies that the classes in question have the property of being model-complete. There are also the following results: quantifier elimination down to primitive formulas, a description of groups interpretable in models of categorical Horn theories, and a description of groups interpretable in models of almost strongly minimal Horn theories. The author proves (contrary to his intention claimed in the paper mentioned above) that there exists a categorical Horn class of structures which cannot be extended to an almost strongly minimal primitive normal class, and to a categorical quasivariety in particular.