Abstract
This work introduces new tools to extend the research framework for Jonsson theories, which form a special subclass of inductive theories. Specifically, we introduce the concept of the Kaiser class and define a new equivalence relation for the study of Jonsson theories, which refines the relation of cosemanticness of the theories. This paper presents an analysis of the main properties of the Kaiser class and KT-equivalent Jonsson theories, addresses the axiomatization of the Kaiser class, and formulates criteria for the perfectness of a Jonsson theory and the cl-normality of a perfect Jonsson theory. Furthermore, we thoroughly examine the algebraic structure of the cosemanticness class of a given Jonsson theory, demonstrate that a distributive lattice can be introduced on this class, and construct specialized sublattices of this lattice. The results obtained can be applied in the study of Jonsson theories and model-theoretic questions with the application of the methods of lattice theory and Universal Algebra.