On Jonsson varieties and quasivarieties
In this paper, new objects of research are identified, both from the standpoint of model theory and from the standpoint of universal algebra. Particularly, the Jonsson spectra of the Jonsson varieties and the Jonsson quasivarieties are considered. Basic concepts of 3 types of convexity are...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Academician Ye.A. Buketov Karaganda University
2021-12-01
|
| Series: | Қарағанды университетінің хабаршысы. Математика сериясы |
| Online Access: | https://mathematics-vestnik.ksu.kz/apart/2021-104-4/15.pdf |
| _version_ | 1827819030809935872 |
|---|---|
| author | A.R. Yeshkeyev |
| author_facet | A.R. Yeshkeyev |
| author_sort | A.R. Yeshkeyev |
| collection | DOAJ |
| description | In this paper, new objects of research are identified, both from the standpoint of model theory and from the standpoint of universal algebra. Particularly, the Jonsson spectra of the Jonsson varieties and the Jonsson quasivarieties are considered. Basic concepts of 3 types of convexity are given: locally convex theory, ϕ(x)-convex theory, J-ϕ(x)-convex theory. Also, the inner and outer worlds of the model of the class of theories are considered. The main result is connected with the question of W. Forrest, which is related to the existential closed ness of an algebraically closed variety. This article gives a sufficient condition for a positive answer to this question. |
| first_indexed | 2024-03-12T01:09:23Z |
| format | Article |
| id | doaj.art-03c91718213a41eeb184e27acebdd2a1 |
| institution | Directory Open Access Journal |
| issn | 2518-7929 2663-5011 |
| language | English |
| last_indexed | 2024-03-12T01:09:23Z |
| publishDate | 2021-12-01 |
| publisher | Academician Ye.A. Buketov Karaganda University |
| record_format | Article |
| series | Қарағанды университетінің хабаршысы. Математика сериясы |
| spelling | doaj.art-03c91718213a41eeb184e27acebdd2a12023-09-14T07:22:20ZengAcademician Ye.A. Buketov Karaganda UniversityҚарағанды университетінің хабаршысы. Математика сериясы2518-79292663-50112021-12-01104415115710.31489/2021M4/151-157On Jonsson varieties and quasivarietiesA.R. Yeshkeyev In this paper, new objects of research are identified, both from the standpoint of model theory and from the standpoint of universal algebra. Particularly, the Jonsson spectra of the Jonsson varieties and the Jonsson quasivarieties are considered. Basic concepts of 3 types of convexity are given: locally convex theory, ϕ(x)-convex theory, J-ϕ(x)-convex theory. Also, the inner and outer worlds of the model of the class of theories are considered. The main result is connected with the question of W. Forrest, which is related to the existential closed ness of an algebraically closed variety. This article gives a sufficient condition for a positive answer to this question.https://mathematics-vestnik.ksu.kz/apart/2021-104-4/15.pdf |
| spellingShingle | A.R. Yeshkeyev On Jonsson varieties and quasivarieties Қарағанды университетінің хабаршысы. Математика сериясы |
| title | On Jonsson varieties and quasivarieties |
| title_full | On Jonsson varieties and quasivarieties |
| title_fullStr | On Jonsson varieties and quasivarieties |
| title_full_unstemmed | On Jonsson varieties and quasivarieties |
| title_short | On Jonsson varieties and quasivarieties |
| title_sort | on jonsson varieties and quasivarieties |
| url | https://mathematics-vestnik.ksu.kz/apart/2021-104-4/15.pdf |
| work_keys_str_mv | AT aryeshkeyev onjonssonvarietiesandquasivarieties |