The hybrids of the ∆-PJ theories

Abstract

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.