On closed classes in partial k-valued logic that contain all polynomials

Abstract Let Polk be the set of all functions of k-valued logic representable by a polynomial modulo k, and let Int (Polk) be the family of all closed classes (with respect to superposition) in the partial k-valued logic containing Polk and consisting only of functions extendable to some function from Polk. Previously the author showed that if k is the product of two different primes, then the family Int (Polk) 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 (Polk) contains an infinitely decreasing (with respect to inclusion) chain of different closed classes.