Computability and Unsolvability

Introduction  
 1. Heuristic Remarks on Decision Problems  
 2. Suggestions to the Reader  
 3. Notational Conventions  
PART 1 - THE GENERAL THEORY OF COMPUTABILITY  
 Ch 1. Computable Functions   
  1. Turing Machines  
  2. Computable Functions and Partially Computable Functions  
  3. Some Examples   
  4. Relatively Computable Functions  
 Ch 2. Operations on Computable Functions  
  1. Preliminary Lemmas  
  2. Composition and Minimalization  
 Ch 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  
 Ch 4. Turing Machines Self-applied  
  1. Arithmetization of the Theory of Turing Machines  
  2. Computability and Recursiveness  
  3. A Universal Turing Machine   
 Ch 5. Unsolvable Decision Problems  
  1. Semicomputable Predicates  
  2. Decision Problems  
  3. Properties of Semicomputable Predicates  
  4. Recursively Enumerable Sets  
  5. Two Recursively Enumerable Sets  
  6. A Set Which Is Not Recursively Enumerable  
PART 2 - APPLICATIONS OF THE GENERAL THEORY  
 Ch 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  
 Ch 7. Diophantine Equations  
  1. Hilbert\'s Tenth Problem  
  2. Arithmetical and Diophantine Predicates  
  3. Arithmetical Representation of Semicomputable Predicates  
 Ch 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  
 Ch 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 2A  
  7. Post\'s Representation Theorem  
 Ch 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
 Ch 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. Some Results from the Elementary Theory of Numbers