  As noticed however first by Chwistek, and later by Ramsey, in the presence of the axiom of reducibility, there is actually no point in introducing the ramified hierarchy at all! It is much simpler to accept impredicative definitions from the start. The simple “extensional” hierarchy of individuals, classes, classes of classes, … is then enough. We get in this way the simpler systems formalised in Gödel 1931 or Church 1940 that were presented above. 