Abstract
It is proved that for any k ≥ 3, any implicatively implicit extension in P<sub>k</sub> contains a class of H<sub>k</sub> homogeneous functions. In each of the 17 implicatively closed classes in P<sub>3</sub>, an implicatively implicitly generating system of functions is constructed. With the exception of the H<sub>3</sub> 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 P<sub>3</sub>.
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