Synopsis
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.
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