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, name...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
A.R. Yeshkeyev [verfasserIn] I.O. Tungushbayeva [verfasserIn] M.T. Kassymetova [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2022 |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
In: Қарағанды университетінің хабаршысы. Математика сериясы - Academician Ye.A. Buketov Karaganda University, 2023, 105(2022), 1 |
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| Übergeordnetes Werk: |
volume:105 ; year:2022 ; number:1 |
| Links: |
Link aufrufen |
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| DOI / URN: |
10.31489/2022m1/127-135 |
|---|
| Katalog-ID: |
DOAJ097993476 |
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| 520 | |a 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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10.31489/2022m1/127-135 doi (DE-627)DOAJ097993476 (DE-599)DOAJeeef8df1d94541f48bbbaa9b97a31d9c DE-627 ger DE-627 rakwb eng QA299.6-433 QA801-939 QA273-280 A.R. Yeshkeyev verfasserin aut Connection between the amalgam and joint embedding properties 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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. Jonsson theory perfect Jonsson theory differential field differential closed field differentially perfect field amalgam property Analysis Analytic mechanics Probabilities. Mathematical statistics I.O. Tungushbayeva verfasserin aut M.T. Kassymetova verfasserin aut In Қарағанды университетінің хабаршысы. Математика сериясы Academician Ye.A. Buketov Karaganda University, 2023 105(2022), 1 (DE-627)DOAJ00015783X 26635011 nnns volume:105 year:2022 number:1 https://doi.org/10.31489/2022m1/127-135 kostenfrei https://doaj.org/article/eeef8df1d94541f48bbbaa9b97a31d9c kostenfrei http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/491 kostenfrei https://doaj.org/toc/2518-7929 Journal toc kostenfrei https://doaj.org/toc/2663-5011 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ AR 105 2022 1 |
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10.31489/2022m1/127-135 doi (DE-627)DOAJ097993476 (DE-599)DOAJeeef8df1d94541f48bbbaa9b97a31d9c DE-627 ger DE-627 rakwb eng QA299.6-433 QA801-939 QA273-280 A.R. Yeshkeyev verfasserin aut Connection between the amalgam and joint embedding properties 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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. Jonsson theory perfect Jonsson theory differential field differential closed field differentially perfect field amalgam property Analysis Analytic mechanics Probabilities. Mathematical statistics I.O. Tungushbayeva verfasserin aut M.T. Kassymetova verfasserin aut In Қарағанды университетінің хабаршысы. Математика сериясы Academician Ye.A. Buketov Karaganda University, 2023 105(2022), 1 (DE-627)DOAJ00015783X 26635011 nnns volume:105 year:2022 number:1 https://doi.org/10.31489/2022m1/127-135 kostenfrei https://doaj.org/article/eeef8df1d94541f48bbbaa9b97a31d9c kostenfrei http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/491 kostenfrei https://doaj.org/toc/2518-7929 Journal toc kostenfrei https://doaj.org/toc/2663-5011 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ AR 105 2022 1 |
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10.31489/2022m1/127-135 doi (DE-627)DOAJ097993476 (DE-599)DOAJeeef8df1d94541f48bbbaa9b97a31d9c DE-627 ger DE-627 rakwb eng QA299.6-433 QA801-939 QA273-280 A.R. Yeshkeyev verfasserin aut Connection between the amalgam and joint embedding properties 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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. Jonsson theory perfect Jonsson theory differential field differential closed field differentially perfect field amalgam property Analysis Analytic mechanics Probabilities. Mathematical statistics I.O. Tungushbayeva verfasserin aut M.T. Kassymetova verfasserin aut In Қарағанды университетінің хабаршысы. Математика сериясы Academician Ye.A. Buketov Karaganda University, 2023 105(2022), 1 (DE-627)DOAJ00015783X 26635011 nnns volume:105 year:2022 number:1 https://doi.org/10.31489/2022m1/127-135 kostenfrei https://doaj.org/article/eeef8df1d94541f48bbbaa9b97a31d9c kostenfrei http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/491 kostenfrei https://doaj.org/toc/2518-7929 Journal toc kostenfrei https://doaj.org/toc/2663-5011 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ AR 105 2022 1 |
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Қарағанды университетінің хабаршысы. Математика сериясы |
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Connection between the amalgam and joint embedding properties |
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(DE-627)DOAJ097993476 (DE-599)DOAJeeef8df1d94541f48bbbaa9b97a31d9c |
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Connection between the amalgam and joint embedding properties |
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A.R. Yeshkeyev |
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Қарағанды университетінің хабаршысы. Математика сериясы |
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A.R. Yeshkeyev I.O. Tungushbayeva M.T. Kassymetova |
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connection between the amalgam and joint embedding properties |
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Connection between the amalgam and joint embedding properties |
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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. |
| abstractGer |
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. |
| abstract_unstemmed |
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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