Book:Martin Davis/Computability and Unsolvability/Second Edition

Subject Matter

 * Logic
 * Mathematical Logic

Contents

 * Preface to the Dover Edition (1982)


 * Preface to the First Edition


 * Glossary of Special Symbols


 * Introduction


 * 1. Heuristic Remarks on Decision Processes
 * 2. Suggestions to the Reader
 * 3. Notational Conventions


 * PART 1: THE GENERAL THEORY OF COMPUTABILITY


 * Chapter 1. Computable Functions
 * 1. Turing Machines
 * 2. Computable Functions and Partially Computable Functions
 * 3. Some Examples
 * 4. Relatively Computable Functions


 * Chapter 2. Operations on Computable Functions
 * 1. Preliminary Lemmas
 * 2. Composition and Minimalization


 * Chapter 3. Recursive Functions
 * 1. Some Classes of Functions
 * 2. Finite Sequences of Natural Numbers
 * 3. Primitive Recursion
 * 4. Primitive Recursive Functions
 * 5. Recursive Sets and Predicates


 * Chapter 4. Turing Machines Self-applied
 * 1. Arithmetization of the Theory of Turing Machines
 * 2. Computability and Recursiveness
 * 3. A Universal Turing Machine


 * Chapter 5. Unsolvable Decision Problems
 * 1. Semicomputable Predicates
 * 2. Decision Problems
 * 3. Properties of Semicomputable Predicates
 * 4. Recursively Semicomputable Predicates
 * 5. Two Recursively Enumerable Sets
 * 6. A Set Which Is Not Recursively Enumerable


 * PART 2: APPLICATIONS OF THE GENERAL THEORY


 * Chapter 6: Combinatorial Problems
 * 1. Combinatorial Systems
 * 2. Turing Machines and Semi-Thue Systems
 * 3. Thue Systems
 * 4. The Word Problem for Semigroups
 * 5. Normal Systems and Post Systems


 * Chapter 7: Diophantine Equations
 * 1. Hilbert's Tenth Problem
 * 2. Arithmetical and Diophantine Predicates
 * 3. Arithmetical Representation of Semicomputable Predicates


 * Chapter 8: Mathematical Logic
 * 1. Logics
 * 2. Incompleteness and Unsolvability Theorems for Logics
 * 3. Arithmetical Logics
 * 4. First-order Logics
 * 5. Partial Propositional Calculi


 * PART 3: FURTHER DEVELOPMENT OF THE GENERAL THEORY


 * Chapter 9. The Kleene Hierarchy
 * 1. The Iteration Theorem
 * 2. Some First Applications of the Iteration Theorem
 * 3. Predicates, Sets, and Functions
 * 4. Strong Reducibility
 * 5. Some Classes of Predicates
 * 6. A Representation Theorem for ${P_2}^A$
 * 7. Post's Representation Theorem


 * Chapter 10. Computable Functionals
 * 1. Functionals
 * 2. Completely Computable Functionals
 * 3. Normal Form Theorems
 * 4. Partially Computable and Computable Functionals
 * 5. Functionals and Relative Recursiveness
 * 6. Decision Problems
 * 7. The Recursion Theorems


 * Chapter 11. The Classification of Unsolvable Decision Problems
 * 1. Reducibility and the Kleene Hierarchy
 * 2. Incomparability
 * 3. Creative Sets and Simple Sets
 * 4. Constructive Ordinals
 * 5. Extensions of the Kleene Hierarchy


 * Appendix 1. Some Results from the Elementary Theory of Numbers


 * Appendix 2. Hilbert's Tenth Problem Is Unsolvable


 * References


 * Index

Source work progress
* : Still to be started.


 * Starting on Appendix $1$ with :


 * : Appendix $1$: Some Results from the Elementary Theory of Numbers: Lemma $1$


 * Check it, make sure nothing has been missed