 As for the axioms of reducibility, Church’s view was that the axioms only reinstate impredicativity for extensional notions and that intensional notions remain unaffected: “Thus the rejection of impredicative definition is annulled in extensional but not in intensional matters”. In this way, RTT with the axioms of reducibility permits the full development of classical number theory and analysis and blocks the semantical paradoxes. This is a view shared by Kripke (2011b) and Myhill (1979).