MODELS OF COMPLETE SOLVABLE THEORIES
С. С. Гончаров, A. T. Nurtazin · 1973
In this paper we study the constructiveness of prime and universal models of complete solvable theories, we obtain a criterion of existence of a strongly constructive prime model of a complete solvable theory, and we present examples of solvable totally transcendental theories in which a prime and a universal model are nonconstructive, whereas a prime model of a solvable categorical theoly is strongly constructive [8]. In §1 we present Goncharov's results on strong constructiveness of prime models, in §2 we present some properties of constructiveness of Boolean algebra proved by Nurtazin, and in §§3 and 4 we present joint results obtained in the stronger version of Nurtazin. § I. Preliminaries Let (~, ~ ) and (f/b z, ¢z ) be constructive models of signature ~ . The definitions of constructiveness and strong constructiveness can be found in [5] and [7].