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Computability

Authors: Tourlakis, George

  • Features extensive and mathematically complete coverage of limitations of logic
  • Explains the inability of computability to effectively detect formal theorems
  • Provides arithmetisation-free proofs of the pillars of computability
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eBook 74,89 €
price for Spain (gross)
  • The eBook version of this title will be available soon
  • Due: December 8, 2021
  • ISBN 978-3-030-83202-5
  • Digitally watermarked, DRM-free
  • Included format:
  • ebooks can be used on all reading devices
Hardcover 93,59 €
price for Spain (gross)
  • Due: December 8, 2021
  • ISBN 978-3-030-83201-8
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this Textbook

This survey of computability theory offers the techniques and tools that computer scientists (as well as mathematicians and philosophers studying the mathematical foundations of computing) need to mathematically analyze computational processes and investigate the theoretical limitations of computing. Beginning with an introduction to the mathematisation of “mechanical process” using URM programs, this textbook explains basic theory such as primitive recursive functions and predicates and sequence-coding, partial recursive functions and predicates, and loop programs. 

Advanced chapters cover the Ackerman function, Tarski’s theorem on the non-representability of truth, Goedel’s incompleteness and Rosser’s incompleteness theorems, two short proofs of the incompleteness theorem that are based on Lob's deliverability conditions, Church’s thesis, the second recursion theorem and applications, a provably recursive universal function for the primitive recursive functions, Oracle computations and various classes of computable functionals, the Arithmetical hierarchy, Turing reducibility and Turing degrees and the priority method, a thorough exposition of various versions of the first recursive theorem, Blum’s complexity, Hierarchies of primitive recursive functions, and a machine-independent characterisation of Cobham's feasibly computable functions.

About the authors

George Tourlakis, PHD, is University Professor of Computer Science and Engineering at York University in Toronto, Canada. He has published extensively in his areas of research interest, which include calculational logic, modal logic, computability, and complexity theory. Dr. Tourlakis is the author of Theory of Computation and Mathematical Logic, both published by Wiley, and Lectures in Logic and Set Theory; Volumes 1 and 2 (Cambridge University Press).

Buy this book

eBook 74,89 €
price for Spain (gross)
  • The eBook version of this title will be available soon
  • Due: December 8, 2021
  • ISBN 978-3-030-83202-5
  • Digitally watermarked, DRM-free
  • Included format:
  • ebooks can be used on all reading devices
Hardcover 93,59 €
price for Spain (gross)
  • Due: December 8, 2021
  • ISBN 978-3-030-83201-8
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Computability
Authors
Copyright
2021
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-83202-5
DOI
10.1007/978-3-030-83202-5
Hardcover ISBN
978-3-030-83201-8
Edition Number
1
Number of Pages
X, 590
Number of Illustrations
11 b/w illustrations, 1 illustrations in colour
Topics