On closed classes in partial k-valued logic that contain the class of monotone functions

Abstract

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.