Closed classes of three-valued logic functions generated by symmetric functions with a bounded number of layers

Closed classes of three-valued logic functions of which a generating system consists of symmetric functions with values in the set $\{0,1\}$ and with value 1 at a bounded subset of layers from $\{1,2\}^n$ are considered. Some criteria for existence of a basis and of a finite basis are obtained for these classes. It is shown how the existence of a basis or of a finite basis depends on the existence of a basis or of a finite basis in subclasses generated by monotonous or non-monotonous functions.