Grundlehren der mathematischen Wissenschaften

Enumerability · Decidability Computability

An Introduction to the Theory of Recursive Functions

Authors: Hermes, Hans

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About this book

Once we have accepted a precise replacement of the concept of algo­ rithm, it becomes possible to attempt the problem whether there exist well-defined collections of problems which cannot be handled by algo­ rithms, and if that is the case, to give concrete cases of this kind. Many such investigations were carried out during the last few decades. The undecidability of arithmetic and other mathematical theories was shown, further the unsolvability of the word problem of group theory. Many mathematicians consider these results and the theory on which they are based to be the most characteristic achievements of mathe­ matics in the first half of the twentieth century. If we grant the legitimacy of the suggested precise replacements of the concept of algorithm and related concepts, then we can say that the mathematicians have shown by strictly mathematical methods that there exist mathematical problems which cannot be dealt with by the methods of calculating mathematics. In view of the important role which mathematics plays today in our conception of the world this fact is of great philosophical interest. Post speaks of a natural law about the "limitations of the mathematicizing power of Homo Sapiens". Here we also find a starting point for the discussion of the question, what the actual creative activity of the mathematician consists in. In this book we shall give an introduction to the theory of algorithms.

Table of contents (7 chapters)

Table of contents (7 chapters)

Buy this book

eBook $84.99
price for USA in USD
  • ISBN 978-3-642-46178-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $109.99
price for USA in USD
  • ISBN 978-3-642-46180-4
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Enumerability · Decidability Computability
Book Subtitle
An Introduction to the Theory of Recursive Functions
Authors
Translated by
Herman, G.T., Plassmann, O.
Series Title
Grundlehren der mathematischen Wissenschaften
Series Volume
127
Copyright
1969
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin · Heidelberg
eBook ISBN
978-3-642-46178-1
DOI
10.1007/978-3-642-46178-1
Softcover ISBN
978-3-642-46180-4
Series ISSN
0072-7830
Edition Number
2
Number of Pages
XII, 250
Topics