 In Russell’s system, the restriction is implemented by characterizing a type not only by the type of its elements but by an additional integer parameter called its “order”. For any object with elements, the order of its type is higher than the order of the type of its elements. Further, the comprehension axiom is restricted so that the condition defining a set of a type of order \(n\) can contain parameters only of types with order \(\le n\) and quantifiers only over types with order \(\lt n\). Russell’s system is further complicated by the fact that it is not a theory of sets, as we noted above, because it also contains relation types (this makes a full account of it here inappropriate). Even if we restrict to types of sets, a simple linear hierarchy of types is not possible if types have order, because each type has “power set” types of each order higher than its own.