The Foundations of Computability Theory

  • Borut Robič

Table of contents

  1. Front Matter
    Pages i-xx
  2. The Roots of Computability Theory

    1. Front Matter
      Pages 1-2
    2. Borut Robič
      Pages 3-7
    3. Borut Robič
      Pages 9-30
    4. Borut Robič
      Pages 31-48
    5. Borut Robič
      Pages 49-66
  3. Classical Computability Theory

    1. Front Matter
      Pages 67-68
    2. Borut Robič
      Pages 69-100
    3. Borut Robič
      Pages 101-142
    4. Borut Robič
      Pages 143-160
    5. Borut Robič
      Pages 161-190
    6. Borut Robič
      Pages 191-215
  4. Relative Computability

    1. Front Matter
      Pages 217-218
    2. Borut Robič
      Pages 219-234
    3. Borut Robič
      Pages 235-244
    4. Borut Robič
      Pages 245-253
    5. Borut Robič
      Pages 269-281
    6. Borut Robič
      Pages 283-293
    7. Borut Robič
      Pages 295-296
  5. Back Matter
    Pages 297-331

About this book


This book offers an original and informative view of the development of fundamental concepts of computability theory. The treatment is put into historical context, emphasizing the motivation for ideas as well as their logical and formal development. In Part I the author introduces computability theory, with chapters on the foundational crisis of mathematics in the early twentieth century, and formalism; in Part II he explains classical computability theory, with chapters on the quest for formalization, the Turing Machine, and early successes such as defining incomputable problems, c.e. (computably enumerable) sets, and developing methods for proving incomputability; in Part III he explains relative computability, with chapters on computation with external help, degrees of unsolvability, the Turing hierarchy of unsolvability, the class of degrees of unsolvability, c.e. degrees and the priority method, and the arithmetical hierarchy.

This is a gentle introduction from the origins of computability theory up to current research, and it will be of value as a textbook and guide for advanced undergraduate and graduate students and researchers in the domains of computability theory and theoretical computer science.


Algorithms Computability theory Models of computation Oracles Relative computability Turing machine

Authors and affiliations

  • Borut Robič
    • 1
  1. 1.Fac of Comp & Inform SciUniversity of LjubljanaLjubljanaSlovenia

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2015
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Computer Science
  • Print ISBN 978-3-662-44807-6
  • Online ISBN 978-3-662-44808-3
  • Buy this book on publisher's site
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IT & Software