The atomic definable subsets of semantic model
In this paper some properties of small models, generally speaking, not necessarily complete theories and their relationship with each other were considered. Under small models we will understand some modifications of the concepts of countable atomic and prime models. These models were defi...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Academician Ye.A. Buketov Karaganda University
2019-06-01
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| Series: | Қарағанды университетінің хабаршысы. Математика сериясы |
| Subjects: | |
| Online Access: | http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/298 |
| _version_ | 1797372687556804608 |
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| author | A.R. Yeshkeyev A.K. Issaeva N.M. Mussina |
| author_facet | A.R. Yeshkeyev A.K. Issaeva N.M. Mussina |
| author_sort | A.R. Yeshkeyev |
| collection | DOAJ |
| description |
In this paper some properties of small models, generally speaking, not necessarily complete theories and their relationship with each other were considered. Under small models we will understand some modifications of the concepts of countable atomic and prime models. These models were defined in the study of countable models of complete theories. Studies were conducted by analogy with the classic result of R. Vaught on countable - prime models of complete theories, but by other technical means. This work is oriented on the syntactic properties of special subsets of the semantic model of some Jonsson theory. A new concept was also introduced, as a model - theoretic «rheostat», in order to obtain results related to the refinement of concept of atomicity within the framework of Jonsson theories. Thus, the main purpose of this article is to formally define this «rheostat» and to obtain on the basis of this concept the results having a relation to the refinement of the concept of atomicity in the frame of Jonsson theories.
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| first_indexed | 2024-03-08T18:39:26Z |
| format | Article |
| id | doaj.art-e9229e2fb4a340a885b3e3bed8e30a67 |
| institution | Directory Open Access Journal |
| issn | 2518-7929 2663-5011 |
| language | English |
| last_indexed | 2024-03-08T18:39:26Z |
| publishDate | 2019-06-01 |
| publisher | Academician Ye.A. Buketov Karaganda University |
| record_format | Article |
| series | Қарағанды университетінің хабаршысы. Математика сериясы |
| spelling | doaj.art-e9229e2fb4a340a885b3e3bed8e30a672023-12-29T10:20:50ZengAcademician Ye.A. Buketov Karaganda UniversityҚарағанды университетінің хабаршысы. Математика сериясы2518-79292663-50112019-06-0194210.31489/2019m2/84-91The atomic definable subsets of semantic modelA.R. YeshkeyevA.K. IssaevaN.M. Mussina In this paper some properties of small models, generally speaking, not necessarily complete theories and their relationship with each other were considered. Under small models we will understand some modifications of the concepts of countable atomic and prime models. These models were defined in the study of countable models of complete theories. Studies were conducted by analogy with the classic result of R. Vaught on countable - prime models of complete theories, but by other technical means. This work is oriented on the syntactic properties of special subsets of the semantic model of some Jonsson theory. A new concept was also introduced, as a model - theoretic «rheostat», in order to obtain results related to the refinement of concept of atomicity within the framework of Jonsson theories. Thus, the main purpose of this article is to formally define this «rheostat» and to obtain on the basis of this concept the results having a relation to the refinement of the concept of atomicity in the frame of Jonsson theories. http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/298Jonsson theorysemantic modeexistentially prime modelatomic modelconvexity |
| spellingShingle | A.R. Yeshkeyev A.K. Issaeva N.M. Mussina The atomic definable subsets of semantic model Қарағанды университетінің хабаршысы. Математика сериясы Jonsson theory semantic mode existentially prime model atomic model convexity |
| title | The atomic definable subsets of semantic model |
| title_full | The atomic definable subsets of semantic model |
| title_fullStr | The atomic definable subsets of semantic model |
| title_full_unstemmed | The atomic definable subsets of semantic model |
| title_short | The atomic definable subsets of semantic model |
| title_sort | atomic definable subsets of semantic model |
| topic | Jonsson theory semantic mode existentially prime model atomic model convexity |
| url | http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/298 |
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