4 The theory of Π¹₁-sets

Kapitel in diesem Buch

1. Frontmatter I
2. Preface VII
3. Contents XI
4. Part I: Fundamental theory
5. 1 An introduction to higher recursion theory 3
6. 2 Hyperarithmetic theory 23
7. 3 Admissibility and constructibility 45
8. 4 The theory of Π¹₁-sets 75
9. 5 Recursion-theoretic forcing 85
10. 6 Set theory 105
11. Part II: The story of Turing degrees
12. 7 Classification of jump operators 131
13. 8 The construction of Π¹₁-sets 147
14. 9 Independence results in recursion theory 165
15. Part III: Hyperarithmetic degrees and perfect set property
16. 10 Rigidity and biinterpretability of hyperdegrees 183
17. 11 Basis theorems 195
18. Part IV: Higher randomness theory
19. 12 Review of classical algorithmic randomness 213
20. 13 More on hyperarithmetic theory 223
21. 14 The theory of higher randomness 245
22. A Open problems 273
23. B An interview with Gerald E. Sacks 275
24. C Notations and symbols 293
25. Bibliography 295
26. Index 303
27. Backmatter 307