Acknowledgements
Interdependence scheme for the chapters
Introduction
Recommended reading
CHAPTER O. PREREQUISITES
CHAPTER 1. BEGINNING MATHEMATICAL LOGIC
1. General considerations
2. Structures and formal languages
3. Higher-order languages
4. Basic syntax
5. Notational conventions
6. Propositional semantics
7. Propositional tableaux
8. The Elimination Theorem for propositional tableaux
9. Completeness of propositional tableaux
10. The propositional calculus
11. The propositional calculus and tableaux
12. Weak completeness of the propositional calculus
13. Strong completeness of the propositional calculus
14. Propositional logic based on "1 and A
15. Propositional logic based on "1, ..*, A and V
16. Historical and bibliographical remarks
CHAPTER 2. FIRST-ORDER LOGIC
1. First-order semantics
2. Freedom and bondage
3. Substitution
4. First-order tableaux
5. Some "book-keeping" lemmas
6. The Elimination Theorem for first-order tableaux
7. Hintikka sets
8. Completeness of first-order tableaux
9. Prenex and Skolem forms
10. Elimination of function symbols
11. Elimination of equality
12. Relativization
13. Virtual terms
14. Historical and bibliographical remarks
CHAPTER 3. FIRST-ORDER LOGIC (CONTINUED)
1. The first-order predicate calculus
2. The first-order predicate calculus and tableaux
3. Completeness of the first-order predicate calculus
4. First-order logic based on 3
5. What have we achieved?
6. Historical and bibliographical remarks
CHAPTER 4. BOOLEAN ALGEBRAS
l. Lattices
2. Boolean algebras
3. Filters and homomorphisms
4. The Stone Representation Theorem
5. Atoms
6. Duality for homomorphisms and continuous mappings...
7. The Rasiowa-Sikorski Theorem
8. Historical and bibliographical remarks
CHAPTER 5. MODEL THEORY
l. Basic ideas of model theory
2. The LSwenheim-Skolem Theorems
3. Ultraproducts
4. Completeness and categoricity
5. Lindenbaum algebras
6. Element types and 0-categoricity
7. Indiscernibles and models with automorphisms
8. Historical and bibliographical remarks
CHAPTER 6. RECURSION THEORY
1. Basic notation and terminology
2. Algorithmic functions and functionals
3. The computer URIM
4. Computable functionals and functions
5. Re, cursive functionals and functions
6. A stockpile of examples
7. Church's Thesis
8. Recursiveness of computable functionals
9. Functionals with several sequence arguments
10. Fundamental theorems
11. Recursively enumerable sets
12. Diophantine relations
13. The Fibonacci sequence
14. The power function
15. Bounded universal quantification
16. The MRDP Theorem and Hilbert's Tenth Problem
17. Historical and bibliographical remarks
CHAPTER 7. LOGIC -- LLqrrATrVE RESULTS
1. General notation and terminology
2. Nonstandard models of fl
3. Arithmeticity
4. Tarski's Theorem
5. Axiomatic theories
6. Baby arithmetic
7. Junior arithmetic
8. A finitely axiomatized theory
9. First-order Peano arithmetic
10. Undecidability
11. Incompleteness
12. Historical and bibliographical remarks
CHAFIng 8. RECURSION THEORY (CONTINUED)
1. The arithmetical hierarchy
2. A result concerning Tt
3. Encoded theories
4. Inseparable pairs of sets
5. Productive and creative sets; reducibility
6. One-one reducibility; recursive isomorphism
7. Turing degrees
8. Post's problem and its solution
9. Historical and bibliographical remarks
CHAPTER 9. INTUTTIONIS'TIC FIRffF-ORDER LOGIC
1. Preliminary discussion
2. Philosophical remark
3. Constructive meaning of sentences
4. Constructive interpretations
5. Intuitionistic tableaux
6. Kripke's semantics
7. The Elimination Theorem for intuitionistic tableaux...
8. Intuitionistic propositional c.qlculus
9. Intuitionistic predicate calculus
10. Completeness
11. Translations from classical to intuitionistic logic
12. The Interpolation Theorem
13. Some results in classical logic
14. Historical and bibliographical remarks
CHAPTER 10. AXIOMAT/C SET THEORY
1. Basic devolopments
2. Ordinals
3. The Axiom of Regularity
4. Cardinality and the Axiom of Choice
5. Reflection Principles...
6. The formalization of satisfaction
7. Absoluteness
8. Constructible sets
9. The consistency of A C and G C H
10. Problems
11. Historical and bibliographical remarks...
CHAPTER 11. NONSTANDARD ANALYSIS
l. Enlargements
2. Zermelo structures and their enlargements .
3. Filters and monads
4. Topology
5. Topological groups
6. The real numbers
7. A methodological discussion
8. Historical and bibliographical remarks . . .
BmUOGRAPHY
GENERAL INDEX
INDEX OF SYMBOLS
