Model-theoretical questions of the Jonsson spectrum

Abstract

In this paper, new concepts are defined in the framework of the study of Jonsson spectrum. We consider a spectrum with respect to the concept of cosemanticness, which is a generalization of elementary equivalence in the class of inductive, generally speaking, incomplete theories. Also, with the help of Jonsson spectrum, the actual directions of the study of Jonsson theories and their model classes are determined, namely, the study of classical questions of model theory, such as the completeness, model completeness, model companion of within the framework of the above conditions, which define a fairly wide subclass of inductive theories, and which Jonsson theories. Therefore, in studying the model-theoretical properties of Jonsson spectrum, we need to clarify the definition of those concepts that naturally arise when we move from the concept of elementary equivalence to the concept of cosemanticness, moreover, both theories and models. Some model-theoretical properties of the Jonsson spectrum are considered. When considering the Jonsson spectrum, all the tasks that are posed in this article make sense and their solution can be useful for solving related problems, because this problem is actively studied in the field of Jonsson theories.