On closed classes of functions of \(k\)-valued logics defined by a single endomorphism. (Russian) Zbl 1249.03018

Marchenkov, S. S.

Diskretn. Anal. Issled. Oper. 16, No. 6, 52-67 (2009).

Summary: We study closed classes in \(P_k\) defined by a single endomorphism. We prove that every such class is positively closed. In the case of non-identical idempotent endomorphisms, the corresponding closed class is positively precomplete in \(P_k\). For \(k=2,3\) all positively precomplete classes in \(P_k\) are defined by such an endomorphism. All positively submaximal classes in \(P_3\) are found.

MSC:

03B50

Many-valued logic

Keywords:

many-valued logic function; endomorphism; positively closed class