Small models of hybrids for special subclasses of Jonsson theories

Abstract

This article presents the result related to the model-theoretic properties of special subsets of the semantic model of some fixed Jonsson theory. The specialty of these sets is due to their definability and closure. Further, we consider fragments of these sets and create a hybrid of these fragments from them. The theory is subject to conditions of strongly convexity and existentially coreness. As a result, the class of existentially closed and algebraically prime models in its non-empty intersection contains a core model. By module of the above conditions, the hybrid of the considered fragments has a model that contains a special core subset, definable closure of which gives a certain existentially closed model, which is an algebraic prime model of the theory under consideration.