Existentially positive Mustafin theories of S-acts over a group
The paper is connected with the study of Jonsson spectrum notion of the fixed class of models of Sacts signature, assuming a group as a monoid of S-acts. The Jonsson spectrum notion is effective when describing theoretical-model properties of algebras classes whose theories admit joint embedding an...
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| Format: | Article |
| Language: | English |
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Academician Ye.A. Buketov Karaganda University
2022-06-01
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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/535 |
| _version_ | 1797372685282443264 |
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| author | A.R. Yeshkeyev O.I. Ulbrikht A.R. Yarullina |
| author_facet | A.R. Yeshkeyev O.I. Ulbrikht A.R. Yarullina |
| author_sort | A.R. Yeshkeyev |
| collection | DOAJ |
| description |
The paper is connected with the study of Jonsson spectrum notion of the fixed class of models of Sacts signature, assuming a group as a monoid of S-acts. The Jonsson spectrum notion is effective when describing theoretical-model properties of algebras classes whose theories admit joint embedding and amalgam properties. It is usually sufficient to consider universal-existential sentences true on models of this class. Up to the present paper, the Jonsson spectrum has tended to deal only with Jonsson theories. The authors of this study define the positive Jonsson spectrum notion, the elements of which can be, non-Jonsson theories. This happens because in the definition of the existentially positive Mustafin theories considered in a given paper involve not only isomorphic embeddings, but also immersions. In this connection, immersions are considered in the definition of amalgam and joint embedding properties. The resulting theories do not necessarily have to be Jonsson. We can observe that the above approach to the Jonsson spectrum study proves to be justified because even in the case of a non-Jonsson theory there exists regular method for finding such Jonsson theory that satisfies previously known notions and results, but that will also be directly related to the existentially positive Mustafin theory in question.
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| first_indexed | 2024-03-08T18:39:23Z |
| format | Article |
| id | doaj.art-dfd5df738e9641f587d18a608e0d755f |
| institution | Directory Open Access Journal |
| issn | 2518-7929 2663-5011 |
| language | English |
| last_indexed | 2024-03-08T18:39:23Z |
| publishDate | 2022-06-01 |
| publisher | Academician Ye.A. Buketov Karaganda University |
| record_format | Article |
| series | Қарағанды университетінің хабаршысы. Математика сериясы |
| spelling | doaj.art-dfd5df738e9641f587d18a608e0d755f2023-12-29T10:19:21ZengAcademician Ye.A. Buketov Karaganda UniversityҚарағанды университетінің хабаршысы. Математика сериясы2518-79292663-50112022-06-01106210.31489/2022m2/172-185Existentially positive Mustafin theories of S-acts over a groupA.R. YeshkeyevO.I. UlbrikhtA.R. Yarullina The paper is connected with the study of Jonsson spectrum notion of the fixed class of models of Sacts signature, assuming a group as a monoid of S-acts. The Jonsson spectrum notion is effective when describing theoretical-model properties of algebras classes whose theories admit joint embedding and amalgam properties. It is usually sufficient to consider universal-existential sentences true on models of this class. Up to the present paper, the Jonsson spectrum has tended to deal only with Jonsson theories. The authors of this study define the positive Jonsson spectrum notion, the elements of which can be, non-Jonsson theories. This happens because in the definition of the existentially positive Mustafin theories considered in a given paper involve not only isomorphic embeddings, but also immersions. In this connection, immersions are considered in the definition of amalgam and joint embedding properties. The resulting theories do not necessarily have to be Jonsson. We can observe that the above approach to the Jonsson spectrum study proves to be justified because even in the case of a non-Jonsson theory there exists regular method for finding such Jonsson theory that satisfies previously known notions and results, but that will also be directly related to the existentially positive Mustafin theory in question. http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/535Jonsson theoryperfect Jonsson theorypositive model theoryJonsson spectrumpositive Jonsson theoryimmersion |
| spellingShingle | A.R. Yeshkeyev O.I. Ulbrikht A.R. Yarullina Existentially positive Mustafin theories of S-acts over a group Қарағанды университетінің хабаршысы. Математика сериясы Jonsson theory perfect Jonsson theory positive model theory Jonsson spectrum positive Jonsson theory immersion |
| title | Existentially positive Mustafin theories of S-acts over a group |
| title_full | Existentially positive Mustafin theories of S-acts over a group |
| title_fullStr | Existentially positive Mustafin theories of S-acts over a group |
| title_full_unstemmed | Existentially positive Mustafin theories of S-acts over a group |
| title_short | Existentially positive Mustafin theories of S-acts over a group |
| title_sort | existentially positive mustafin theories of s acts over a group |
| topic | Jonsson theory perfect Jonsson theory positive model theory Jonsson spectrum positive Jonsson theory immersion |
| url | http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/535 |
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