43 research outputs found
Existential prime convex Jonsson theories and their models
No full textThis article is devoted to the study of the model - theoretic properties of special subclasses of Jonsson theories and their classes of models. Namely, introduce a new class of Jonsson theories is existentially prime convex Jonsson theories. The notion of convexity of theory was previously known, it was introduced by A.Robinson. The notion of existential simplicity introduced by the author of this article. Both conditions form a broad natural classes of theories. Thus two natural restrictions on Jonsson define a new class of theories with rich model - theoretic properties. Besides defined formulation of the problem, which define a new direction in the study Jonsson theories
Method of the rheostat for studying properties of fragments of theoretical sets
No full textIn 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 property of independence for Jonsson sets
No full textThe 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
Strongly minimal Jonsson sets and their properties
No full textThis article introduced and considered the Johnson sets and their fragments. And respectively was considered strongly minimal Jonsson sets. On this basis, introduced 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 base and further we develop technique for Jonssonien analog of theorem on uncountable categoricity
The similarity of closures of Jonsson sets
No full textThis 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
Some properties of Morly rank over Jonsson sets
No full textThis 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
Model-theoretical questions of the Jonsson spectrum
No full textIn 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 Properties of Similarity for Jonsson’s Theories and Their Models
No full textActually, we study the connections of the ∆-PJ-theories with their centers. The properties of various companions of some ∆-PJ-theories and their connection with this theory are considered. Also the similarity of the central types of ∆-PJ-theories in the enriched language is considered. In the class of perfect ∆-PJ-theories the conditions of coincidence of algebraic primeness with some sort of atomic models are found. In the class of ∆-PJ-theories, the concepts of syntactic and semantic similarities are introduced and the results on the relationship of these similarities in this class with their centers are obtained
About central types and the cosemanticness of the ∆-PM fragment of the Jonsson set
No full textThis article is concerned with the enrichment of the signature. In own time, when studying the stability of the theory and the concept of an elementary pair of models, Mustafin T.G. had noticed that these things are related to each other and he introduced the concept T ∗-stability [1]. In fact, some enrichment of the signature is considered. Generally speaking, the theories obtained in the extended language are incomplete, therefore, the number of such completions of these theories is sought. This number also determines stability in the sense of T ∗-stability. It was noted by E.A.Palyutin in [2] that the concept of T ∗-stability is not invariant with respect to definability of type. But we know that in the classical sense of S.Sellach the stability of the theory is invariant with respect to the definability of type. Therefore Palyutin E.A. had introduced the concept E ∗-stability, which preserved the definability of type..
The properties of central-orbital types of EPSCJ theories
No full textThis article, in its content, refers to the study of the theoretical - model properties of the Jonsson theories. A new approach to this study is proposed. As a new notion, the idea of a central - orbital type is used. When studying Jonsson theories are taken into account the following facts:Syntactic, concerning the Jonsson theories and the Jonsson subsets of the semantic model of the Jonsson theory under consideration.In addition, a special role in the syntactic sense is played by the enrichment of the signature associated with the given Jonsson sets. The semantic aspect of the issues under consideration is primarily concerned with the notion of convexity, strong convexity, and existential primeness.Although these definitions are related to theory, in fact we are dealing with different types of models that are existentially closed
