The properties of central types with respect to enrichment by Jonsson set

Abstract

The main results of the article are for a new class of theories, namely existential prime strongly convex Jonsson theories. This class is quite broad in terms of algebra, for example it includes the class of all Abelian groups and groups. This article examines the issues relating to the following subjects. The language on considered a signature adds a new predicate symbol which reflects the presence of the Jonsson set. The concept of Jonsson sets in Jonsson theory is a generalization of the concept of the dimension of the linear space. T.G. Mustafin in due time, introduced and proved the basic properties of the syntactic and semantic similarity. In this paper, in the extended language we have similare to the results for the considered theories. In this direction, the main results of the work are the following results: The coincidence of P–stability for the prototype and its central-type center. The equivalence of syntactic similarity of existentially EP SCJ compleate theories and syntactical similarity of their centers was consedered. From this it can be seen a lot of useful facts. In particular semantic similarity. As well as a list of semantic properties, which are stored at the semantic similarity. For example, the semantic properties that invariant properties of the first order applies Morley rank of the central type.