Sets with an infinite number of {{{...}}}

Question

In pure mathematics, is there such a set with an infinite number of {{{...}}}? Is there a name for them? What are their properties? Letting $$R=\{x∶x\notin x\},$$ does Russell's paradox hold for this sort of sets, {{{...}}}?

Answer 1

The Axiom of Regularity implies there is no infinite descending sequence of sets, so the answer to your infinite curly brace question is "no".