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On the setP  k  ∗$\begin{array}{} \displaystyle P_k^* \end{array}$    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  ⩾ 2, the number of implicative closed classes inP  k  ∗$\begin{array}{} \displaystyle P_k^* \end{array}$    is finite. For any  k  ⩾ 2, inP  k  ∗$\begin{array}{} \displaystyle P_k^* \end{array}$    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 inP  3  ∗$\begin{array}{} \displaystyle P_3^* \end{array}$   .

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