On some implicitly precomplete classes of monotone functions in $P_k$

The paper is concerned with the completeness problem in implicit expressibility in a multi-valued logics $P_k$. For each $k\geq 2$ and any nontrivial order relation on the set $\{0,1,\dots,k-1\}$ we find two implicitly precomplete classes of functions which are monotone with respect to this order