The hybrids of the ∆ − PJ theories

When studying Jonsson theories, which are a wide subclass of inductive theories, it becomes necessary to study the so - called Jonsson sets. Similar problems are considered both in model theory and in universal algebra. This topic is related to the study of model - theoretical properties of positive fragments. These fragments are a definable closure of special subsets of the semantic model of a fixed Jonsson theory. In this article are considered model - theoretical properties of a new class of theories, namely ∆ - PJ theories of countable first - order language. These are theories that are obtained from ∆ - PJ theories by replacing in the definition of ∆- PJ theories of morphisms (∆ - continuities) with morphisms (∆ - immersions). A number of results were obtained, ∆ - PJ fragments, ∆ - PJ sets, hybrids of ∆ - PJ theories. All questions considered in this article are relevant in the study of Jonsson theories and their model classes.