Companions of the fragments in the Jonsson enrichment

Abstract

In this article we consider the properties of central types for the existentially prime strongly convex Jonsson theories in some extension. This class of theories is a subclass of a broad class of Jonsson theories. In particular, the Jonsson theories include the class of all fields of a fixed characteristic. In the given work, problems related to the classical problems of the general Model Theory concerning the following topics were considered. First of all, we note the values of enrichment. Using the one-place predicate, the Jonsson subset is singled out and the concepts of P -stability and various kinds of similarities are considered for the Jonsson completion. The following results were obtained:Coincidence of P - stability for a prototype of the central type and its center. Equivalence of syntactic similarity of companions of fragments of Jonsson enrichment and syntactic similarity of their centers.The above notion of stability has an applied value for studying the properties of the central types in this enrichment. In the second place, it is necessary to note the significance of the concept of the central type in this enrichment.The very idea of a central type presupposes an additional description of the properties of incomplete Jonsson theories by means of central completion. The Jonsson subsets of the semantic model of the existentially prime convex Jonsson theory have good theoretic-model properties. This concerns the Morley rank and it is preserved in the syntactic and semantic similarity of the above theories.