Geodesic
Implicatively precomplete sets of multioperations defined on a set of three elements
The Bulletin of Irkutsk State University. Series Mathematics, Tome 51 (2025), pp. 130-140

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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.
Keywords: closure, multioperation, closed set, completeness, representability.
Mots-clés : composition 
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     author = {V. I. Panteleev},
     title = {Implicatively precomplete sets of multioperations defined on a set of three elements},
     journal = {The Bulletin of Irkutsk State University. Series Mathematics},
     pages = {130--140},
     publisher = {mathdoc},
     volume = {51},
     year = {2025},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIGUM_2025_51_a8/}
}
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V. I. Panteleev. Implicatively precomplete sets of multioperations defined on a set of three elements. The Bulletin of Irkutsk State University. Series Mathematics, Tome 51 (2025), pp. 130-140. http://geodesic.mathdoc.fr/item/IIGUM_2025_51_a8/