Limited combinatorial-selector sets

This article discusses the issue of classification of their own subsets of $N =\lbrace0,1,2,3,... \rbrace $ by means of partial Boolean functions. For an arbitrary partial Boolean function $ \beta $ defines the notion of $ \beta $-limited combinatorial-selector set, which is a generalization of the concept of $ \beta $-selector set [1]. Fully describe the classes of these sets, the relationship between these classes by inclusion.