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The Foundations of Computability Theory

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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.

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Series Title

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Call Number

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Publisher

Springer Berlin, Heidelberg : Springer Berlin, Heidelberg., 2015

Collation

XX, 331

Language

English

ISBN/ISSN

978-3-662-44808-3

Classification

NONE

Content Type

text

Media Type

computer

Carrier Type

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Edition

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Subject(s)

Computational Mathematics and Numerical Analysis

Specific Detail Info

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Statement of Responsibility

Borut Robič

Other Information

Cataloger

Jemadi

Source

https://link.springer.com/content/pdf/10.1007/978-3-662-44808-3.pdf?pdf=button

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