The Limits of Computation

Abstract This article provides a survey of key papers that characterise computable functions, but also some novel insights as follows. It is argued the power algorithms at least strong functions can be proved to totally in type-theoretic translations subsystems second-order Zermelo Fraenkel set theory. Moreover, it claimed typed systems lambda calculus give rise naturally functional interpretation rich types and hierarchy ordinal recursive functionals arbitrary type reduced by substitution natural number functions.