It is proved that for any k ≥ 3, any implicatively implicit extension in P_k contains a class of H_k homogeneous functions. In each of the 17 implicatively closed classes in P₃, an implicatively implicitly generating system of functions is constructed. With the exception of the H₃ class, each of the systems consists of one or two no more than two-place functions. A one-place function is specified, the implicatively implicit extension of which is different from any implicatively closed class in P₃.

implicatively implicit basis, implicatively closed class, three-valued logic

Mathematical problems and theory of numerical methods

Marchenkov Sergey Seraphimovich,  ,  orcid.org/0000-0003-3716-5661,  Lomonosov Moscow State University