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Erschienen in:
1987 | OriginalPaper | Buchkapitel
Type 2 Computability Models
verfasst von : Prof. Dr. Klaus Weihrauch
Erschienen in: Computability
Verlag: Springer Berlin Heidelberg
Enthalten in: Professional Book Archive
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In Type 1 recursion theory we have defined computability explicitly on numbers and on words and we have shown that both approaches are essentially equivalent (see Theorem 1.7.5). Computability on other denumerable sets can be reduced to computability on ℕ via numberings or notations. In this chapter we shall introduce three explicit definitions of Type 2 computability and prove that they are essentially equivalent. Any “natural” kind of computability on some other Type 2 set should be reducible to any one of these three definitions by means of a representation.