To found the current set theory, it has been necessary to remove some paradoxes like the well-known Russel paradox. It was thus necessary to clarify why things like $$\{x : x \notin x\}$$ can't reasonably be considered as sets. Several propositions were made like our usual ZFC with a limitation of the size but another was the "positivism paradigm". I know that the global idea of this theory is to treat separately the two symbols $\notin$ and $\in$ and to state that one can't refer negatively to itself but I can't find after many research a good purely mathematical text which is quite exhaustive about this subject. Many philosophical texts can be found but I wan't the pure mathematical approach with rigourous definitions.
Any help will be greatly appreciated.