 We have objects of type 0, for individuals, objects of type 1, for classes of individuals, objects of type 2, for classes of classes of individuals, and so on. Functions of two or more arguments, like relations, need not be included among primitive objects since one can define relations to be classes of ordered pairs, and ordered pairs to be classes of classes. For example, the ordered pair of individuals a, b can be defined to be \(\{\{a\},\{a,b\}\}\) where \(\{x,y\}\) denotes the class whose sole elements are \(x\) and \(y\). (Wiener 1914 had suggested a similar reduction of relations to classes.) In this system, all propositions have the form \(a(b)\), where \(a\) is a sign of type \(n+1\) and \(b\) a sign of type \(n\). Thus this system is built on the concept of an arbitrary class or subset of objects of a given domain and on the fact that the collection of all subsets of the given domain can form a new domain of the next type. Starting from a given domain of individuals, this process is then iterated. As emphasised for instance in Scott 1993, in set theory this process of forming subsets is iterated into the transfinite.