Chapter 18. An impassable barrier

Chapters in this book

1. Frontmatter i
2. Acknowledgments v
3. Table of Contents vii
4. Chapter 1. The impredicativity of induction 1
5. Chapter 2. Logical terminology 3
6. Chapter 3. The axioms of arithmetic 8
7. Chapter 4. Order 10
8. Chapter 5. Induction by relativization 12
9. Chapter 6. Interpretability in Robinson's theory 16
10. Chapter 7. Bounded induction 23
11. Chapter 8. The bounded least number principle 29
12. Chapter 9. The euclidean algorithm 32
13. Chapter 10. Encoding 36
14. Chapter 11. Bounded separation and minimum 43
15. Chapter 12. Sets and functions 46
16. Chapter 13. Exponential functions 51
17. Chapter 14. Exponentiation 54
18. Chapter 15. A stronger relativization scheme 60
19. Chapter 16. Bounds on exponential functions 64
20. Chapter 17. Bounded replacement 70
21. Chapter 18. An impassable barrier 73
22. Chapter 19. Sequences 82
23. Chapter 20. Cardinality 90
24. Chapter 21. Existence of sets 95
25. Chapter 22. Semibounded Replacement 98
26. Chapter 23. Formulas 101
27. Chapter 24. Proofs 111
28. Chapter 25. Derived rules of inference 115
29. Chapter 26. Special constants 134
30. Chapter 27. Extensions by definition 136
31. Chapter 28. Interpretations 152
32. Chapter 29. The arithmetization of arithmetic 157
33. Chapter 30. The consistency theorem 162
34. Chapter 31. Is exponentiation total? 173
35. Chapter 32. A modified Hilbert program 178
36. Bibliography 181
37. General index 183
38. Index of defining axioms 186