Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- 1 Introduction
- 2 Arithmetical preliminaries
- 3 Primes and proofs
- 4 The language of arithmetic
- 5 The language of analysis
- 6 Ordinals and inductive definitions
- 7 Formal languages and the definition of truth
- 8 Logic and theories
- 9 Peano Arithmetic and computability
- 10 Elementary and classical analysis
- 11 The recursion theorem and ordinal notations
- 12 The incompleteness theorems
- 13 Iterated consistency
- 14 Iterated reflection
- 15 Iterated iteration and inexhaustibility
- References
- Index
6 - Ordinals and inductive definitions
Published online by Cambridge University Press: 30 March 2017
- Frontmatter
- Dedication
- Contents
- Preface
- 1 Introduction
- 2 Arithmetical preliminaries
- 3 Primes and proofs
- 4 The language of arithmetic
- 5 The language of analysis
- 6 Ordinals and inductive definitions
- 7 Formal languages and the definition of truth
- 8 Logic and theories
- 9 Peano Arithmetic and computability
- 10 Elementary and classical analysis
- 11 The recursion theorem and ordinal notations
- 12 The incompleteness theorems
- 13 Iterated consistency
- 14 Iterated reflection
- 15 Iterated iteration and inexhaustibility
- References
- Index
Summary
- Type
- Chapter
- Information
- InexhaustibilityA Non-Exhaustive Treatment, pp. 87 - 104Publisher: Cambridge University PressPrint publication year: 2004