Companions of fragments in admissible enrichments

Abstract

In this paper, model-theoretic properties of companions of fragments of special subsets in admissible enrichments are considered. Admissible enrichments are understood as enrichments of a signature that preserve the basic syntactic properties of the Jonsson theory under consideration. The study of the properties of companions of the Jonsson theory is related to the classical problematics of studying inductive theories, which was determined at the time by one of the founders of the theory of models A. Robinson. In this paper, the main properties of companion fragments of definable subsets of the semantic model of a given Jonsson theory is categoricity and it is considered.