Turing Computability Theory and Applications /

• Main Author: Soare, Robert I. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2016.
• Series: Theory and Applications of Computability, In cooperation with the association Computability in Europe,
• Subjects: Computer science.; Computers.; Computer science > Mathematics.; Mathematical logic.; Computer Science.; Theory of Computation.; Mathematics of Computing.; Mathematical Logic and Foundations.

Turing's famous 1936 paper introduced a formal definition of a computing machine, a Turing machine. This model led to both the development of actual computers and to computability theory, the study of what machines can and cannot compute. This book presents classical computability theory from T...

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 C.E. Sets
• Chap. 6 Oracle Constructions and Forcing
• Chap. 7 The Finite Injury Method
• Part II Trees and Π01 Classes
• Chap. 8 Open and Closed Classes
• Chap. 9 Basis Theorems
• Chap. 10 Peano Arithmetic and Π01-Classes
• Chap. 11 Randomness and Π01-Classes
• Part III Minimal Degrees
• Chap. 12 Minimal Degrees Below Øʹʹ
• Chap. 13 Minimal Degrees Below Øʹ
• Part IV Games in Computability Theory
• Chap. 14 Banach-Mazur Games
• Chap. 15 Gale-Stewart Games
• Chap. 16 More Lachlan Games
• Part V History of Computability
• Chap. 17 History of Computability
• References
• Index.