 Though these notions are relative to the formal system, it has turned out that strong and weak representability are extremely stable. Quite independently of the particular formal system chosen, exactly the decidable, or recursive, sets (relations) are strongly representable, and exactly the semi-decidable, or recursively enumerable sets (relations) are weakly representable. This holds for all formalized systems which contain Robinson arithmetic Q, from Robinson arithmetic itself to the strongest axioms systems of set theory like ZFC and beyond (as long as they are (recursively) axiomatizable). Instead of using the notion of “representability”, Gödel took a different approach by speaking of sets being “decidable in a formal system \(F\)” (“entscheidungsdefinit”). If the proofs of \(F\) are systematically generated, it will be eventually determined, for any given number \(\boldsymbol{n}\), whether it belongs to \(S\) or not—given that \(S\) is strongly representable in \(F\). 