Hyperarithmetical functions and algebraicity

Kapitel in diesem Buch

1. Frontmatter I
2. Preface V
3. Table of contents VII
4. Priority method in generalized computability 1
5. Polynomial-time versus computable Boolean algebras 15
6. The proof-theoretic strength of the Dushnik-Miller Theorem for countable linear orders 55
7. Effectively nowhere simple relations on computable structures 59
8. Jump traces with large gaps 71
9. Weak recursive degrees and a problem of Spector 81
10. Compositions of permutations and algorithmic reducibilities 89
11. Some properties of majorant-computability 97
12. Hyperarithmetical functions and algebraicity 115
13. Weak presentations of fields not extendible to recursive presentations 131
14. Jumps of Ʃ⁰₂-high e-degrees and properly Ʃ⁰₂ e-degrees 157
15. Enumeration reducibility and the problem of the nontotal property of e-degrees 173
16. Algebras of recursive functions 193
17. Σ₂ Induction and cuppable degrees 215
18. Open problems 229
19. List of talks 235
20. List of contributors 237
21. Backmatter 240