Mathematical logic

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PREFACE, 1981

PREFACE TO THE REVISED EDITION

PREFACE

CONTENTS

Introduction

CHAPTER ONE. Statements

1. Conjunction, Alternation, and Denial

2. The Conditional

3. Iterated Composition

4. Use versus Mention

5. Statements about Statements

6. Quasi-Quotation

7. Parentheses and Dots

8. Reduction to Three Primitives

9. Reduction to One Primitive

10. Tautology

11. Selected Tautologous Forms

CHAPTER TWO. Quantification

12. The Quantifier

13. FormulÃ?

14. Bondage, Freedom, Closure 15. Axioms of Quantification16. Theorems

17. Metatheorems

18. Substitutivity of the Biconditional

19. Existential Quantification

20. Distribution of Quantifiers

21. Alphabetic Variance

CHAPTER THREE. Terms

22. Class and Member

23. Logical FormulÃ?

24. Abstraction

25. Identity

26. Abstraction Resumed

27. Descriptions and Names

CHAPTER FOUR. Extended Theory of Classes

28. Stratification

29. Further Axioms of Membership

30. Substitutivity of Identity

31. Substitution for Variables 32. Further Consequences33. Logical Product, Sum, Complement

34. Inclusion

35. Unit Classes

CHAPTER FIVE. Relations

36. Pairs and Relations

37. Abstraction of Relations

38. Converse, Image, Relative Product

39. The Ancestral

40. Functions

41. Abstraction of Functions

42. Identity and Membership as Relations

CHAPTER SIX. Number

43. Zero, One, Successor

44. Natural Numbers

45. Counter Sets

46. Finite and Infinite

47. Powers of Relations

48. Arithmetical Sum, Product, Power 49. Familiar Identities of Arithmetic50. Ratios

51. Real Numbers

52. Further Extensions

CHAPTER SEVEN. Syntax

53. Formality

54. The Syntactical Primitive

55. Protosyntax

56. Formula and Matrix Defined

57. Axioms of Quantification Defined

58. Theorem Defined

59. Protosyntax Self-Applied

60. Incompleteness

APPENDIX. Theorem versus Metatheorem

List of Definitions

List of Theorems and Metatheorems

Bibliographical References

Index of Proper Names

Index of Subjects