Computability pp 216-226 | Cite as

Effective Numberings

  • Klaus Weihrauch
Part of the EATCS Monographs on Theoretical Computer Science book series (EATCS, volume 9)


In Chapter 2.2 we have defined how a numbering v of a set S induces a computability theory on the set S. We have shown that the numbering v of a set S is determined uniquely (up to equivalence) by the computability theory induced by it (Lemma 2.2.8, Conclusion 2.2.9). In this chapter we shall study for which effectivity conditions numberings satisfying these conditions exist. As a main result we shall show that for sets which are defined as closures numberings defined via generation trees are natural.


Computability Theory Standard Numbering Easy Induction Bibliographical Note Partial Recursive Function 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • Klaus Weihrauch
    • 1
  1. 1.FB Mathematik und InformatikFern Universität HagenHagenGermany

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