Geodesic
Completeness criterion with respect to the enumeration closure operator in the three-valued logic
Diskretnaya Matematika, Tome 33 (2021) no. 2, pp. 86-99

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The enumeration closure operator (the $\Pi$-operator) is considered on the set $P_k$ of functions of the $k$-valued logic. It is proved that, for any $k\geqslant 2$, any positively precomplete class in $P_k$ is also $\Pi$-precomplete. It is also established that there are no other $\Pi$-precomplete classes in the three-valued logic.
Keywords: enumeration closure operator, functions of three-valued logic. 
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     author = {S. S. Marchenkov and V. A. Prostov},
     title = {Completeness criterion with respect to the enumeration closure operator in the three-valued logic},
     journal = {Diskretnaya Matematika},
     pages = {86--99},
     publisher = {mathdoc},
     volume = {33},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2021_33_2_a6/}
}
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S. S. Marchenkov; V. A. Prostov. Completeness criterion with respect to the enumeration closure operator in the three-valued logic. Diskretnaya Matematika, Tome 33 (2021) no. 2, pp. 86-99. http://geodesic.mathdoc.fr/item/DM_2021_33_2_a6/