Syntactic similarity of definable closures of Jonsson sets

Abstract

In the framework of the classification of the Jonsson theories concept of interpretability and admissibility in the language of the semantic triple of the Jonsson theory was considered. A description of the syntactic and semantic similarity of perfect fragments of Jonsson subsets of the semantic model of the existential-prime convex Jonsson theory was obtained. Some model-theoretic properties for Jonsson’s theories are considered. Such theories, as group theory, the theory of Abelian groups, the theory of Boolean algebra, the theory of ordered sets, the theory of polygons, and many others satisfies Jonsson’s properties.