On closed classes in partial k-valued logic that contain the class of monotone functions
Valeriy B. Alekseev · Discrete Mathematics and Applications · 2019
Abstract 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.