Existentially prime Jonsson quasivarieties and their Jonsson spectra
This article is devoted to the study of Jonsson quasivarieties in a signature enriched with new predicate and constant symbols. New concepts of semantic Jonsson quasivariety and fragment-conservativeness of the center of the Jonsson theory are introduced. The cosemanticness classes of the J...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Academician Ye.A. Buketov Karaganda University
2022-12-01
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| Series: | Қарағанды университетінің хабаршысы. Математика сериясы |
| Online Access: | https://mathematics-vestnik.ksu.kz/apart/2022-108-4/11.pdf |
| _version_ | 1797687479582588928 |
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| author | A.R. Yeshkeyev I.O. Tungushbayeva S.M. Amanbekov |
| author_facet | A.R. Yeshkeyev I.O. Tungushbayeva S.M. Amanbekov |
| author_sort | A.R. Yeshkeyev |
| collection | DOAJ |
| description | This article is devoted to the study of Jonsson quasivarieties in a signature enriched with new predicate and constant symbols. New concepts of semantic Jonsson quasivariety and fragment-conservativeness of the center of the Jonsson theory are introduced. The cosemanticness classes of the Jonsson spectrum constructed for a semantic Jonsson quasvariety are considered. In this case, the Kaiser hull of the semantic Jonsson quasivariety is assumed to be existentially prime. By constructing a central type for classes of theories from the Jonsson spectrum, the following results are formulated and proved. In the first main result, the necessary and sufficient condition is given for the center of the cosemanticness class of an existentially prime semantic Jonsson quasivariety to be λ-stable. The second result is the criterion for the center of the class of theories to be ω-categorical in the enriched language. The obtained theorems can be useful in continuing studies of various Jonsson algebras, in particular, Jonsson quasivarieties. |
| first_indexed | 2024-03-12T01:18:33Z |
| format | Article |
| id | doaj.art-6fa3879d4dc744a6af80776346da1ea9 |
| institution | Directory Open Access Journal |
| issn | 2518-7929 2663-5011 |
| language | English |
| last_indexed | 2024-03-12T01:18:33Z |
| publishDate | 2022-12-01 |
| publisher | Academician Ye.A. Buketov Karaganda University |
| record_format | Article |
| series | Қарағанды университетінің хабаршысы. Математика сериясы |
| spelling | doaj.art-6fa3879d4dc744a6af80776346da1ea92023-09-13T09:53:25ZengAcademician Ye.A. Buketov Karaganda UniversityҚарағанды университетінің хабаршысы. Математика сериясы2518-79292663-50112022-12-01108411712410.31489/2022M4/117-124Existentially prime Jonsson quasivarieties and their Jonsson spectraA.R. Yeshkeyev I.O. TungushbayevaS.M. Amanbekov This article is devoted to the study of Jonsson quasivarieties in a signature enriched with new predicate and constant symbols. New concepts of semantic Jonsson quasivariety and fragment-conservativeness of the center of the Jonsson theory are introduced. The cosemanticness classes of the Jonsson spectrum constructed for a semantic Jonsson quasvariety are considered. In this case, the Kaiser hull of the semantic Jonsson quasivariety is assumed to be existentially prime. By constructing a central type for classes of theories from the Jonsson spectrum, the following results are formulated and proved. In the first main result, the necessary and sufficient condition is given for the center of the cosemanticness class of an existentially prime semantic Jonsson quasivariety to be λ-stable. The second result is the criterion for the center of the class of theories to be ω-categorical in the enriched language. The obtained theorems can be useful in continuing studies of various Jonsson algebras, in particular, Jonsson quasivarieties.https://mathematics-vestnik.ksu.kz/apart/2022-108-4/11.pdf |
| spellingShingle | A.R. Yeshkeyev I.O. Tungushbayeva S.M. Amanbekov Existentially prime Jonsson quasivarieties and their Jonsson spectra Қарағанды университетінің хабаршысы. Математика сериясы |
| title | Existentially prime Jonsson quasivarieties and their Jonsson spectra |
| title_full | Existentially prime Jonsson quasivarieties and their Jonsson spectra |
| title_fullStr | Existentially prime Jonsson quasivarieties and their Jonsson spectra |
| title_full_unstemmed | Existentially prime Jonsson quasivarieties and their Jonsson spectra |
| title_short | Existentially prime Jonsson quasivarieties and their Jonsson spectra |
| title_sort | existentially prime jonsson quasivarieties and their jonsson spectra |
| url | https://mathematics-vestnik.ksu.kz/apart/2022-108-4/11.pdf |
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