EN|RU Volume 16, No 6, 2009, P. 52-67 UDC 519.716 S. S. Marchenkov On closed classes of a $k$-valued logics functions defined by a single endomorphism Abstract: The closed classes in $P_k$ defined by a single endomorphism are investigated. It is proved that every such class is positive closed. In the case of nonidentical idempotent endomorphism the corresponding class is positive precomplete in $P_k$. For $k=2,3$ all positive precomplete classes in $P_k$ are defined by the same endomorphisms. All positive submaximal classes in $P_3$ are found. Bibl. 11. Keywords: many-valued logic function, endomorphism, positive closed classes. Marchenkov Sergey Serafimovich 1 1. Lomonosov Moscow State University, Vorob’evy ghory, 119992 Moscow, Russia e-mail: mathcyb@cs.msu.su © Sobolev Institute of Mathematics, 2015