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 simple existential strongly Jonsson convex theories. This class is quite broad in terms of algebra, for example it includes the class of all Abelian groups and simple groups. This article examines the issues relating to the following subjects. The language is considered a signature adds a new predicate symbol which reflects the presence of of the Jonsson set. In turn, the presence of so many in the model provides a basis for the dimensional ratios of elements and subsets as concept Jonsson sets in Jonsson theory is a generalization of the concept of the dimension of the linear space. T.G. Mustafin in due time he introduced and proved the basic properties of the syntactic and semantic similarity. In this paper, in the extended language are similar 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 existentially committed EP SCJ full of theories and syntactical similarity of their centers. 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.