  which is impredicative: we have defined a predicate \(L\) by an existential quantification over all predicates. In the ramified hierarchy, if \(C\) is a class of first-order classes of rationals, then \(L\) will be a second-order class of rationals. One obtains then not one notion or real numbers, but real numbers of different orders 1, 2, … The least upper bound of a collection of reals of order 1 will then be at least of order 2 in general. 