As a key characteristics induced by the structure, each object is assigned a rank between 0 and a fixed limit ordinal ϖ. Objects with rank ϖ are unbounded, the remaining ones are bounded. For unbounded objects x, the images of {x} under ϵ and ϵ are coincident. Therefore, object membership is formed as the union
It is shown that every basic structure is a substructure of an (ϖ+1)-superstructure and thus can be embedded in the von Neumann universe of sets. The inheritance root r appears as the ϖ-th cumulation of urelement-like sets. The above equality for object membership is expressed as
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