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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Irkutsk State University
2025-03-01
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| Series: | Известия Иркутского государственного университета: Серия "Математика" |
| Subjects: | |
| Online Access: | https://mathizv.isu.ru/en/article/file?id=1526 |
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| Summary: | 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. |
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| ISSN: | 1997-7670 2541-8785 |