Abstract
Abstract The theory of the computable functions establishes the scope and limits of computation by means of algorithms on the set N = (0,1,2,...) of natural numbers. It is based on the assumption that this set of data, equipped with some very simple operations, forms an algebraic structure that is computable in some absolute sense: the data are concrete objects and the operations on the data are computable. An objective of the theory is to analyse and classify the functions and sets that can be defined, using a variety of models of computation and formal systems, over some fundamental algebras of natural numbers.
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