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Computer Science - Theoretical Computer Science | Computability Theory and Applications - The Art of Classical Computability

Computability Theory and Applications

The Art of Classical Computability

Soare, Robert I.

2015, Approx. 430 p.

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ISBN 978-3-642-31933-4

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  • Author is among the world's leading authorities on the topic of computability
  • Content has been thoroughly class-tested for many years by hundreds of lecturers and teachers in this field
  • Emphasizes the art of computability, that is, a skill to be practiced but also important an esthetic sense of beauty and taste in mathematics
This book emphasizes three very important concepts: computability, as opposed to recursion or induction; classical computability, i.e., algorithmic functions on certain countable structures in the original sense of Turing and Post; and the art of computability, i.e., a skill to be practiced, but also important an esthetic sense of beauty and taste in mathematics.

Content Level » Graduate

Keywords » Alan Turing - Banach--Mazur games - Gale--Stewart games - automorphisms - classical art - classical computability - computability - computably enumerable sets - definability - index sets - infinite injury - lachlan games - minimal pairs - pinball machines - tree method - turing reducibility

Related subjects » Mathematics - Theoretical Computer Science

Table of contents 

Part I Foundations of Computability.- Chap. 1 Defining Computability.- Chap. 2 Computably Enumerable Sets.- Chap. 3 Turing Reducibility.- Chap. 4 The Arithmetical Hierarchy.- Chap. 5 Classifying Computably Enumerable Sets.- Chap. 6 Oracle Constructions and Forcing.- Chap. 7 The Finite Injury Priority Method.- Part II Infinite Injury and the Tree Method.- Chap. 8 Infinite Injury.- Chap. 9 The Tree Method and Minimal Pairs.- Chap. 10 More Tree Proofs.- Part III Games in Computability.- Chap. 11 Banach--Mazur Games.- Chap. 12 Gale--Stewart Games.- Chap. 13 Lachlan Games.- Chap. 14 Index Sets of Computably Enumerable Sets.- Chap. 15 Pinball Machines.- Part IV Definability and Automorphisms.- Chap. 16 Definable Properties of Computably Enumerable Sets.- Chap. 17 Automorphisms of Computably Enumerable Sets.- Part V The History and Art of Computability.- Chap. 18 The History and Art of Computability.- Chap. 19 Classical Computability and Classical Art.- App. A Standard Definitions.- App. B Hints for Exercises.- Bibliography.- Indexes.

Distribution rights 

Distribution rights for India: Researchco Book Centre, New Delhi, India

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