Geodesic
On closed classes in partial $k$-valued logic that contain all polynomials
Diskretnaya Matematika, Tome 33 (2021) no. 2, pp. 6-19

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Let $Pol_k$ be the set of all functions of $k$-valued logic representable by a polynomial modulo $k$, and let $Int(Pol_k)$ be the family of all closed classes (with respect to superposition) in the partial $k$-valued logic containing $Pol_k$ and consisting only of functions extendable to some function from $Pol_k$. Previously the author showed that if $k$ is the product of two different primes, then the family $Int(Pol_k)$ consists of 7 closed classes. In this paper, it is proved that if $k$ has at least 3 different prime divisors, then the family $Int(Pol_k)$ contains an infinitely decreasing (with respect to inclusion) chain of different closed classes.
Keywords: $k$-valued logic, partial $k$-valued logic, closed class, polynomial, predicate. 
@article{DM_2021_33_2_a1,
     author = {V. B. Alekseev},
     title = {On closed classes in partial $k$-valued logic that contain all polynomials},
     journal = {Diskretnaya Matematika},
     pages = {6--19},
     publisher = {mathdoc},
     volume = {33},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2021_33_2_a1/}
}
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V. B. Alekseev. On closed classes in partial $k$-valued logic that contain all polynomials. Diskretnaya Matematika, Tome 33 (2021) no. 2, pp. 6-19. http://geodesic.mathdoc.fr/item/DM_2021_33_2_a1/