9. Other Approaches to Computable Analysis

In the preceeding chapters we have developed Type-2 Theory of effectivity, TTE, which provides tools for studying various aspects of computability in analysis and, ill particular, offers a “natural” definition of computable real functions. In contrast to the computable number functions where numerous definitions coincide (Church’s Thesis) and alternatives are no longer considered seriously [Rog67, Odi89] several partly non-equivalent approaches to computable analysis have been proposed and are still being investigated. In this chapter we outline the concepts of some of these approaches and compare them with TTE. For avoiding additional technical framework we will express the original definitions in the terms used in this book whenever advisable.