Сore Jonsson theories

Abstract

The article concerns the description the new concept as core of Jonsson theories, also their combinations, which admit a core model in the class of existentially closed models of this theory. Along with core the property of an existentially algebraically prime theory is considered as an additional property to core Jonsson theory. This article also discusses some combinations of Johnson’s theories, where the authors tried to transfer some results from [1] to Johnson’s theories that satisfy the definition of core or EAP, or their combinations. From the definition of the core and the existentially algebraic primeness of Johnson theory, it can be noted that the core model from [1] in the framework of the study of any Johnson theory will be a unique and rigidly embedded model of the theory were considered. And thus, such a solution to the problem with respect to core models is considered for the first time.