On closed classes in partial k -valued logic that contain all polynomials
Valeriy B. Alekseev · Discrete Mathematics and Applications · 2021
Abstract 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.