# Mathematical logic

Harvard University Press, Cambridge, MA, ©1981
1 online resource (xii, 346 pages)
9780674042469, 0674042468
646832519
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
Electronic reproduction, [Place of publication not identified], HathiTrust Digital Library, 2010
English