On the action of the implicative closure operator on the set of partial functions of the multivalued logic

On the set $P_k^*$ of partial functions of the $k$-valued logic, we consider the implicative closure operator, which is the extension of the parametric closure operator via the logical implication. It is proved that, for any $k\geqslant 2$, the number of implicative closed classes in $P_k^*$ is finite. For any $k\geqslant 2$, in $P_k^*$ two series of implicative closed classes are defined. We show that these two series exhaust all implicative precomplete classes. We also identify all 8 atoms of the lattice of implicative closed classes in $P_3^*$.