Abstract
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.
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© 1987 Springer-Verlag Berlin Heidelberg
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Weihrauch, K. (1987). Type 2 Computability Models. In: Computability. EATCS Monographs on Theoretical Computer Science, vol 9. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-69965-8_24
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DOI: https://doi.org/10.1007/978-3-642-69965-8_24
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-69967-2
Online ISBN: 978-3-642-69965-8
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