Completeness criterion with respect to the enumeration closure operator in the three-valued logic

The enumeration closure operator (the $\Pi$-operator) is considered on the set $P_k$ of functions of the $k$-valued logic. It is proved that, for any $k\geqslant 2$, any positively precomplete class in $P_k$ is also $\Pi$-precomplete. It is also established that there are no other $\Pi$-precomplete classes in the three-valued logic.