Abstract
The hybrids of the ∆ -P J 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 ∆ -P J theories of countable first-order language.These are theories that are obtained from ∆-P J theories by replacing in the definition of ∆ -P J theories of morphisms (∆-continuities) with morphisms (∆-immersions).A number of results were obtained, ∆ -P J fragments, ∆ -P J sets, hybrids of ∆ -P J theories.All questions considered in this article are relevant in the study of Jonsson theories and their model classes.