The characterization of the class formula_166 of all subsets of a set formula_94 involves unbounded universal quantification, namely formula_168. Here formula_169 has been defined in terms of the membership predicate formula_2 above. So in such a set theoretical framework, the power class is defined not in a bottom-up construction from its constituents (like an algorithm on a list, e.g. formula_171) but via a comprehension over all sets. The formula_172-valued functions on a set formula_94 inject into formula_174 and thus correspond to its decidable subsets.