Implicatively Precomplete Sets of Multioperations Defined on a Set of Three Elements
We study the completeness criterion on the set of rank-3 multioperations with respect to the implicative closure operator. The problem is a special case of the problem of finite classification of multioperations defined on an arbitrary set. A description of all precomplete sets is obtained. The expr...
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Irkutsk State University
2025-03-01
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| Series: | Известия Иркутского государственного университета: Серия "Математика" |
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| Online Access: | https://mathizv.isu.ru/en/article/file?id=1526 |
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| author | V.I. Panteleev |
| author_facet | V.I. Panteleev |
| author_sort | V.I. Panteleev |
| collection | DOAJ |
| description | We study the completeness criterion on the set of rank-3 multioperations with respect to the implicative closure operator. The problem is a special case of the problem of finite classification of multioperations defined on an arbitrary set. A description of all precomplete sets is obtained. The expressive possibilities of the operator are described, including the conditions under which a set of operations implicatively generates all sets of multoperations. The obtained result can be used in the study of multioperations defined on an arbitrary set. |
| format | Article |
| id | doaj-art-342f4db0fec14e7db0223656848fa3d6 |
| institution | DOAJ |
| issn | 1997-7670 2541-8785 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Irkutsk State University |
| record_format | Article |
| series | Известия Иркутского государственного университета: Серия "Математика" |
| spelling | doaj-art-342f4db0fec14e7db0223656848fa3d62025-08-20T03:02:10ZengIrkutsk State UniversityИзвестия Иркутского государственного университета: Серия "Математика"1997-76702541-87852025-03-01511130140https://doi.org/10.26516/1997-7670.2025.51.130Implicatively Precomplete Sets of Multioperations Defined on a Set of Three ElementsV.I. PanteleevWe study the completeness criterion on the set of rank-3 multioperations with respect to the implicative closure operator. The problem is a special case of the problem of finite classification of multioperations defined on an arbitrary set. A description of all precomplete sets is obtained. The expressive possibilities of the operator are described, including the conditions under which a set of operations implicatively generates all sets of multoperations. The obtained result can be used in the study of multioperations defined on an arbitrary set.https://mathizv.isu.ru/en/article/file?id=1526closuremultioperationclosed setcompositioncompletenessrepresentability |
| spellingShingle | V.I. Panteleev Implicatively Precomplete Sets of Multioperations Defined on a Set of Three Elements Известия Иркутского государственного университета: Серия "Математика" closure multioperation closed set composition completeness representability |
| title | Implicatively Precomplete Sets of Multioperations Defined on a Set of Three Elements |
| title_full | Implicatively Precomplete Sets of Multioperations Defined on a Set of Three Elements |
| title_fullStr | Implicatively Precomplete Sets of Multioperations Defined on a Set of Three Elements |
| title_full_unstemmed | Implicatively Precomplete Sets of Multioperations Defined on a Set of Three Elements |
| title_short | Implicatively Precomplete Sets of Multioperations Defined on a Set of Three Elements |
| title_sort | implicatively precomplete sets of multioperations defined on a set of three elements |
| topic | closure multioperation closed set composition completeness representability |
| url | https://mathizv.isu.ru/en/article/file?id=1526 |
| work_keys_str_mv | AT vipanteleev implicativelyprecompletesetsofmultioperationsdefinedonasetofthreeelements |