∇-cl-atomic and prime sets

Abstract

In this article the model-theoretic properties of special formula subsets of the semantic model of some fixed Jonsson theory are considered. The main purpose of this paper is the study of concepts of models’ primeness and atomness in the study of inductive theories which admit the property of joint embedding and amalgama property. For this purpose is determined special sets, each element of which realise some type which is which is the main type in the sense of an existential formulas. Definable closures of such sets form an existential closed model. The main result obtained in this paper describes the properties of atomic and prime sets regarding strongly convex Jonsson theories.