Unrolling Construction

The structure $⟨M,N,\in ⟩$ may be reduced to the structure $⟨M\cup N,\in ⟩$. This does not preserve structure and may result in paradoxes if not carefully stratified.

A set is $0$-class, a proper-class is $1$-class that is also not a set, an object which contains proper-classes as elements are $2$-classes (also called ‘conglomerates’)…,etc.

Note: An $n$-class is also $n+1$-class. This process is cumulative

Intuition: Unrolling construction allows for second-order structures (i.e., class structures of theories $MK$ and $NGB$) to be translated into first-order structures via ‘unpacking’ them.

References

Philosophy of Sets & Proper-Classes