Abstract
This chapter presents an expository treatment of the elements of recursive function theory. The chapter also discusses informal computability, Turing machines, Church's thesis, universal machines, and normal form. The simplest conception of recursive functions is effectively computable functions. There are many equivalent ways of formulating the definition of recursiveness. A version phrased in terms of imaginary computing machines was given by the English mathematician Alan Turing. The chapter also discusses oracles and functional, recursive enumerability, logic and recursion theory, degrees of unsolvability, definability and recursion, creative and lesser sets, and recursive analogs of classical objects.
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