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The Foundations of Computability Theory

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Cover of 'The Foundations of Computability Theory'

Table of Contents

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    Book Overview
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    Chapter 1 Introduction
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    Chapter 2 The Foundational Crisis of Mathematics
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    Chapter 3 Formalism
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    Chapter 4 Hilbert’s Attempt at Recovery
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    Chapter 5 The Quest for a Formalization
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    Chapter 6 The Turing Machine
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    Chapter 7 The First Basic Results
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    Chapter 8 Incomputable Problems
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    Chapter 9 Methods of Proving Incomputability
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    Chapter 10 Computation with External Help
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    Chapter 11 Degrees of Unsolvability
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    Chapter 12 The Turing Hierarchy of Unsolvability
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    Chapter 13 The Class $$ \mathcal{D} $$ of Degrees of Unsolvability
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    Chapter 14 C.E. Degrees and the Priority Method
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    Chapter 15 The Arithmetical Hierarchy
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    Chapter 16 Computability (Church-Turing) Thesis Revisited
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    Chapter 17 Further Reading
Attention for Chapter 15: The Arithmetical Hierarchy
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