Properties of a stability for positive Jonsson theories

Actually, we study the connections of the Δ-PM-theories with their centers in the enrich signature. The properties of various companions of some Δ-PM-theories and their connection with this theory are considered on the language of the central types of positive Jonsson theory

Method of the rheostat for studying properties of fragments of theoretical sets

In this article discusses the model-theoretical properties of fragments of theoretical sets and the rheostat method. These two concepts: theoretical set and rheostat are new. The study of this topic in the framework of the study of Jonsson theories, the Jonsson spectrum, classes of existentially closed models of such fragments is a new promising class of problems and their solution is closely related to many problems that once defined the classical problems of model theory. The purpose of this article is to determine the rheostat of the transition from complete theory to Jonsson theory, which will be consistent with the corresponding concepts for any α and any α-Jonsson theory. For this we define a theoretical set. On the basis of research by the author formulated a model-theoretical definition of the concept of a rheostat in the transition from complete theories to ϕ(x)-theoretically convex Jonsson sets. Also was formulated an application of h-syntactic similarity to α-Jonsson theories

The similarity of closures of Jonsson sets

This article is devoted to the study model - theoretic properties of special closures of Jonsson sets. That is considered a syntactic similarity of Jonsson theories for universal existential sentences which true in these models. Due to the fact that the fragments of Jonsson sets are Jonsson theories, such an approach for the study of such theories is acceptable. Besides define the certain range of questions not previously are risen in studies such theories and its of their models classes

On Jonsson varieties and quasivarieties

In this paper, new objects of research are identified, both from the standpoint of model theory and from the standpoint of universal algebra. Particularly, the Jonsson spectra of the Jonsson varieties and the Jonsson quasivarieties are considered. Basic concepts of 3 types of convexity are given: locally convex theory, ϕ(x)-convex theory,  J-ϕ(x)-convex theory. Also, the inner and outer worlds of the model of the class of theories are considered. The main result is connected with the question of W. Forrest, which is related to the existential closedness of an algebraically closed variety. This article gives a sufficient condition for a positive answer to this question

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

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

On Jonsson varieties and quasivarieties

In this paper, new objects of research are identified, both from the standpoint of model theory and from the standpoint of universal algebra. Particularly, the Jonsson spectra of the Jonsson varieties and the Jonsson quasivarieties are considered. Basic concepts of 3 types of convexity are given: locally convex theory, ϕ(x)-convex theory, J-ϕ(x)-convex theory. Also, the inner and outer worlds of the model of the class of theories are considered. The main result is connected with the question of W. Forrest, which is related to the existential closed ness of an algebraically closed variety. This article gives a sufficient condition for a positive answer to this question

Some properties of Morly rank over Jonsson sets

This article introduced and discussed the concepts of minimal Jonsson sets and respectively strongly minimal Jonsson sets. On this basis, it introduces the concept of the independence of special subsets of existentially closed submodel of the semantic model. The notion of independence leads to the concept of basis and then we have an analogue of the Jonsson theorem on uncountable categorical. The concept of strongly minimal, as for sets and so for theories played a decisive role in obtaining results on the description of uncountable - categorical theories. It is well known that Jonsson Theories are a natural subclass of the broad class of theories, as a class of inductive theories. As is known, the basic examples theories of algebra are examples of inductive theories, and they tend to represent an example of incomplete theories. This modern apparatus of Model Theory developed mainly for complete theories, so nowadays technique studying incomplete theories noticeable poorer than for complete theories. Thus, all of the above says that the study of model - theoretic properties Jonsson theories is an actual problem. This article describes the basic properties of the Morley rank over Jonsson subsets of semantic model for some Jonsson theory

Convex fragmens of strongly minimal Jonsson sets

This article introduced and discussed the concepts of minimal Jonsson sets and respectively strongly minimal Jonsson sets. On this basis, we introduce the concept of independence of special subsets of existentially closed submodel of semantic model. The concept of independence leads to the concept of basis and then we have the Jonsson analogue of the theorem on uncountable categoricity

Model-theoretical questions of the Jonsson spectrum

In this paper, new concepts are defined in the framework of the study of Jonsson spectrum. We consider a spectrum with respect to the concept of cosemanticness, which is a generalization of elementary equivalence in the class of inductive, generally speaking, incomplete theories. Also, with the help of Jonsson spectrum, the actual directions of the study of Jonsson theories and their model classes are determined, namely, the study of classical questions of model theory, such as the completeness, model completeness, model companion of within the framework of the above conditions, which define a fairly wide subclass of inductive theories, and which Jonsson theories. Therefore, in studying the model - theoretical properties of Jonsson spectrum, we need to clarify the definition of those concepts that naturally arise when we move from the concept of elementary equivalence to the concept of cosemanticness, moreover, both theories and models. Some model - theoretical properties of the Jonsson spectrum are considered. When considering the Jonsson spectrum, all the tasks that are posed in this article make sense and their solution can be useful for solving related problems, because this problem is actively studied in the field of Jonsson theories

The property of independence for Jonsson sets

The studies carried out in this article are connected with the description of model - theoretic properties of some, generally speaking, incomplete classes of theories that make a subclass of inductive theories. These theories are well studied both in algebra and in the theory of models. They are called Jonsson’s theories. To study these theories there is introduced a new research approach, namely: on the submultitudes of a semantic model of Jonsson’s theory there are separated special multitudes that are, firstly, realizations of some existential formula, secondly, the closing of the set gives us the basic set of some existentially closed submodel of the semantic model. Besides, there is developed a technique of studying the central orbital types. It is well known that the perfect Jonsson theory enough comfortable for model - theoretic researches. Practically, in the perfect case, we can say that with the help of semantic method, we can give a specific description of these objects (Jonsson theory and class its existentially closed models). In this article we will give the notion of forking for fragment of fixing Jonsson theory. The nonforking extensions will be the «Mfree» ones. Also we considered for the notion of independence many desirable properties like monotonicity, transitivity, finite basis and symmetry