Limited-combinatorial sets

This article discusses the issue of classification of their own subsets of $\mathbb{N}=\{0,1,2,3,\ldots\}$ by means of partial Boolean functions. For an arbitrary partial Boolean function $\beta$ defines the notion of $\beta$-limited combinatorial set, which is a generalization of the concept of $\beta$-combinatorial set [1]. Fully describe the classes of these sets, the relationship between these classes by inclusion.