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Recursive Functions

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

Abstract

In the last two chapters we considered the properties of μ-recursive functions. It was shown that the class of μ-recursive functions is the same as the class of Turing-computable functions and so the same as the class of the functions which are computable in the intuitive sense. Thus, we can say that the concept of μ-recursive function, just like that of Turing-computable function, is a precise replacement of the concept of computable function. Another concept which can be considered to be a precise replacement of the concept of computable function (and which historically precedes the concept of μ-recursive function) is the concept of recursive function (Herbrand, Gödel, Kleene). After the definition of recursiveness (in § 19) we shall show in the two following paragraphs that the class of μ-recursive functions coincides with the class of recursive functions.

Keywords

Function Variable Recursive Function Computable Function Regular System Finite System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Kleene, S. C.: General Recursive Functions of Natural Numbers. Math. Ann. 112, 727–742 (1936).Google Scholar
  2. Kalmar, L.: Über ein Problem, betreffend die Definition des Begriffes der allgemeinrekursiven Funktion. Z. math. Logik 1, 93–96 (1955). (Here we find the example dealt with in Section 7.)Google 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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