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