The Equivalence of Turing-Computability and μ-Recursiveness

  • Hans Hermes
Conference paper
Part of the Die Grundlehren der Mathematischen Wissenschaften book series (GL, volume 127)


We have already emphasized in the preface that the equivalence of the suggested precise replacements of the intuitive concept of computable function can be shown by purely mathematical considerations. We shall do this in this chapter for the concept of Turing-computable function and the concept of μ-recursive function. (Cf. also Chapter 5 and § 30.) An equivalence proof of this kind generally leads to a standard representation of computable functions. Thus, we shall obtain (in § 18) Kleene’s normal form theorem.


Turing Machine Regular Function Recursive Function Computable Function Inductive Definition 
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  1. Kleene, S. C.: General Recursive Functions of Natural Numbers. Math. Ann. 112, 727–742 (1936). (Normal form theorem.)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1965

Authors and Affiliations

  • Hans Hermes
    • 1
  1. 1.University of MünsterMünster i. W.Germany

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