Geodesic
On closed classes in partial $k$-valued logic that contain the class of monotone functions
Diskretnaya Matematika, Tome 30 (2018) no. 2, pp. 3-13

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Let $A$ be a precomplete class (a maximal clone) in $k$-valued logic and $T(A)$ be the family of all closed classes (under superposition) in partial $k$-valued logic that contain $A$. A simple test is put forward capable of finding out from a partial order defining the precomplete class $A$ of monotone functions whether the family $T(A)$ is finite or infinite. This completes the solution of the problem of finiteness of $T(A)$ for all precomplete classes of $k$-valued logic. The proof depends on new families of closed classes founded by the author of the present paper.
Keywords: $k$-valued logic, partial $k$-valued logic, closed class, precomplete class, monotone function. 
@article{DM_2018_30_2_a0,
     author = {V. B. Alekseev},
     title = {On closed classes in partial $k$-valued logic that contain the class of monotone functions},
     journal = {Diskretnaya Matematika},
     pages = {3--13},
     publisher = {mathdoc},
     volume = {30},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2018_30_2_a0/}
}
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V. B. Alekseev. On closed classes in partial $k$-valued logic that contain the class of monotone functions. Diskretnaya Matematika, Tome 30 (2018) no. 2, pp. 3-13. http://geodesic.mathdoc.fr/item/DM_2018_30_2_a0/