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Enumerability, Decidability, Computability

An Introduction to the Theory of Recursive Functions

  • Conference proceedings
  • © 1965

Overview

Authors:
  1. Hans Hermes

    1. University of Münster, Germany

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Part of the book series: Grundlehren der mathematischen Wissenschaften (GL, volume 127)

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Table of contents (7 papers)

  1. Front Matter

    Pages II-X
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  2. Introductory Reflections on Algorithms

    • Hans Hermes
    Pages 1-30

  3. Turing Machines

    • Hans Hermes
    Pages 31-59

  4. μ-Recursive Functions

    • Hans Hermes
    Pages 59-93

  5. The Equivalence of Turing-Computability and μ-Recursiveness

    • Hans Hermes
    Pages 93-112

  6. Recursive Functions

    • Hans Hermes
    Pages 113-140

  7. Undecidable Predicates

    • Hans Hermes
    Pages 141-187

  8. Miscellaneous

    • Hans Hermes
    Pages 187-240

  9. Back Matter

    Pages 241-245
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Keywords

About this book

The task of developing algorithms to solve problems has always been considered by mathematicians to be an especially interesting and im­ portant one. Normally an algorithm is applicable only to a narrowly limited group of problems. Such is for instance the Euclidean algorithm, which determines the greatest common divisor of two numbers, or the well-known procedure which is used to obtain the square root of a natural number in decimal notation. The more important these special algorithms are, all the more desirable it seems to have algorithms of a greater range of applicability at one's disposal. Throughout the centuries, attempts to provide algorithms applicable as widely as possible were rather unsuc­ cessful. It was only in the second half of the last century that the first appreciable advance took place. Namely, an important group of the inferences of the logic of predicates was given in the form of a calculus. (Here the Boolean algebra played an essential pioneer role. ) One could now perhaps have conjectured that all mathematical problems are solvable by algorithms. However, well-known, yet unsolved problems (problems like the word problem of group theory or Hilbert's tenth problem, which considers the question of solvability of Diophantine equations) were warnings to be careful. Nevertheless, the impulse had been given to search for the essence of algorithms. Leibniz already had inquired into this problem, but without success.

Authors and Affiliations

  • University of Münster, Germany

    Hans Hermes

Bibliographic Information

  • Book Title: Enumerability, Decidability, Computability

  • Book Subtitle: An Introduction to the Theory of Recursive Functions

  • Authors: Hans Hermes

  • Series Title: Grundlehren der mathematischen Wissenschaften

  • DOI: https://doi.org/10.1007/978-3-662-11686-9

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1965

  • eBook ISBN: 978-3-662-11686-9Published: 14 March 2013

  • Series ISSN: 0072-7830

  • Series E-ISSN: 2196-9701

  • Edition Number: 1

  • Number of Pages: X, 245

  • Additional Information: Title of the original German edition: Aufzählbarkeit, Entscheidbarkeit, Berechenbarkeit

  • Topics: Functional Analysis, Mathematics, general

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