Connection between the amalgam and joint embedding properties
The paper aims to study the model-theoretic properties of differentially closed fields of zero and positive characteristics in framework of study of Jonsson theories. The main attention is paid to the amalgam and joint embedding properties of DCF theory as specific features of Jonsson theories, nam...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Academician Ye.A. Buketov Karaganda University
2022-03-01
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| Series: | Қарағанды университетінің хабаршысы. Математика сериясы |
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| Online Access: | http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/491 |
| _version_ | 1797372690201313280 |
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| author | A.R. Yeshkeyev I.O. Tungushbayeva M.T. Kassymetova |
| author_facet | A.R. Yeshkeyev I.O. Tungushbayeva M.T. Kassymetova |
| author_sort | A.R. Yeshkeyev |
| collection | DOAJ |
| description |
The paper aims to study the model-theoretic properties of differentially closed fields of zero and positive characteristics in framework of study of Jonsson theories. The main attention is paid to the amalgam and joint embedding properties of DCF theory as specific features of Jonsson theories, namely, the implication of JEP from AP. The necessity is identified and justified by importance of information about the mentioned properties for certain theories to obtain their detailed model-theoretic description. At the same time, the current apparatus for studying incomplete theories (Jonsson theories are generally incomplete) is not sufficiently developed. The following results have been obtained: The subclasses of Jonsson theories are determined from the point of view of joint embedding and amalgam properties. Within the exploration of one of these classes, namely the AP-theories, that the theories of differential and differentially closed fields of characteristic 0, differentially perfect and differentially closed fields of fixed positive characteristic are shown to be Jonsson and perfect. Along with this, the theory of differential fields of positive characteristic is considered as an example of an AP-theory that is not Jonsson, but has the model companion, which is perfect Jonsson theory, and the sufficient condition for the theory of differential fields is formulated in the context of being Jonsson.
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| first_indexed | 2024-03-08T18:39:28Z |
| format | Article |
| id | doaj.art-eeef8df1d94541f48bbbaa9b97a31d9c |
| institution | Directory Open Access Journal |
| issn | 2518-7929 2663-5011 |
| language | English |
| last_indexed | 2024-03-08T18:39:28Z |
| publishDate | 2022-03-01 |
| publisher | Academician Ye.A. Buketov Karaganda University |
| record_format | Article |
| series | Қарағанды университетінің хабаршысы. Математика сериясы |
| spelling | doaj.art-eeef8df1d94541f48bbbaa9b97a31d9c2023-12-29T10:19:30ZengAcademician Ye.A. Buketov Karaganda UniversityҚарағанды университетінің хабаршысы. Математика сериясы2518-79292663-50112022-03-01105110.31489/2022m1/127-135Connection between the amalgam and joint embedding propertiesA.R. YeshkeyevI.O. TungushbayevaM.T. Kassymetova The paper aims to study the model-theoretic properties of differentially closed fields of zero and positive characteristics in framework of study of Jonsson theories. The main attention is paid to the amalgam and joint embedding properties of DCF theory as specific features of Jonsson theories, namely, the implication of JEP from AP. The necessity is identified and justified by importance of information about the mentioned properties for certain theories to obtain their detailed model-theoretic description. At the same time, the current apparatus for studying incomplete theories (Jonsson theories are generally incomplete) is not sufficiently developed. The following results have been obtained: The subclasses of Jonsson theories are determined from the point of view of joint embedding and amalgam properties. Within the exploration of one of these classes, namely the AP-theories, that the theories of differential and differentially closed fields of characteristic 0, differentially perfect and differentially closed fields of fixed positive characteristic are shown to be Jonsson and perfect. Along with this, the theory of differential fields of positive characteristic is considered as an example of an AP-theory that is not Jonsson, but has the model companion, which is perfect Jonsson theory, and the sufficient condition for the theory of differential fields is formulated in the context of being Jonsson. http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/491Jonsson theoryperfect Jonsson theorydifferential fielddifferential closed fielddifferentially perfect fieldamalgam property |
| spellingShingle | A.R. Yeshkeyev I.O. Tungushbayeva M.T. Kassymetova Connection between the amalgam and joint embedding properties Қарағанды университетінің хабаршысы. Математика сериясы Jonsson theory perfect Jonsson theory differential field differential closed field differentially perfect field amalgam property |
| title | Connection between the amalgam and joint embedding properties |
| title_full | Connection between the amalgam and joint embedding properties |
| title_fullStr | Connection between the amalgam and joint embedding properties |
| title_full_unstemmed | Connection between the amalgam and joint embedding properties |
| title_short | Connection between the amalgam and joint embedding properties |
| title_sort | connection between the amalgam and joint embedding properties |
| topic | Jonsson theory perfect Jonsson theory differential field differential closed field differentially perfect field amalgam property |
| url | http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/491 |
| work_keys_str_mv | AT aryeshkeyev connectionbetweentheamalgamandjointembeddingproperties AT iotungushbayeva connectionbetweentheamalgamandjointembeddingproperties AT mtkassymetova connectionbetweentheamalgamandjointembeddingproperties |