CHAPTER 0．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．Propositionallogic based on ？ and∧

15．Propositional logic based on？,→,∧and ∨

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

1．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

1．Basic ideas of model theory

2．The L？wenheim-Skolem Theorems

3．Ultraproducts

4．Completeness and categoricity

5．Lindenbaum algebras

6．Element types and ？-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．Recursive 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—LIMITATIVE RESULTS

1．General notation and terminology

2．Nonstandard models of Ω

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

CHAPTER 8．RECURSION THEORY(CONTINUED)

1．The arithmetical hierarchy

2．A result concerning TΩ

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．INTUITIONISTIC FIRST-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 calculus

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．AXIOMATIC SET THEORY

1．Basic developments

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 AC and GCH

10．Problems

11．Historical and bibliographical remarks

CHAPTER 11．NONSTANDARD ANALYSIS

1．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

BIBLIOGRAPHY

GENERAL INDFX

INDEX OF SYMBOLS