The Foundations of Computability Theory

The Foundations of Computability Theory

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 theo...

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Bibliographic Details
Main Author: Robič, Borut (Author)
Corporate Author: SpringerLink (Online service)
Format: Electronic eBook
Language:English
Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2015.
Edition:1st ed. 2015.
Subjects:
Computer science.
Computers.
Computer science > Mathematics.
Computer mathematics.
Computer Science.
Theory of Computation.
Mathematics of Computing.
Computational Mathematics and Numerical Analysis.
Online Access:Full Text via HEAL-Link
Table of Contents:
  • Introduction
  • The Foundational Crisis of Mathematics
  • Formalism
  • Hilbert’s Attempt at Recovery
  • The Quest for a Formalization
  • The Turing Machine
  • The First Basic Results
  • Incomputable Problems
  • Methods of Proving the Incomputability
  • Computation with External Help
  • Degrees of Unsolvability
  • The Turing Hierarchy of Unsolvability
  • The Class D of Degrees of Unsolvability
  • C.E. Degrees and the Priority Method
  • The Arithmetical Hierarchy
  • Further Reading
  • App. A, Mathematical Background
  • References
  • Index.

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