Computability theory and degree structures
This thesis mainly studies the thin-free degrees. We show the technique to construct a thin-free degree, and construct a hyperimmune-free minimal thin-free degrees below 0'', and a nonbranching thin-free r.e. degree. We also show that any 1-generic degree below 0' is not thin-free, wh...
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Thesis-Doctor of Philosophy |
| Language: | English |
| Published: |
Nanyang Technological University
2020
|
| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/139815 |
| _version_ | 1811686628020715520 |
|---|---|
| author | Yuan, Bowen |
| author2 | Wu Guohua |
| author_facet | Wu Guohua Yuan, Bowen |
| author_sort | Yuan, Bowen |
| collection | NTU |
| description | This thesis mainly studies the thin-free degrees. We show the technique to construct a thin-free degree, and construct a hyperimmune-free minimal thin-free degrees below 0'', and a nonbranching thin-free r.e. degree. We also show that any 1-generic degree below 0' is not thin-free, while any nonzero degree below a 2-generic degree is thin-free. |
| first_indexed | 2024-10-01T05:03:26Z |
| format | Thesis-Doctor of Philosophy |
| id | ntu-10356/139815 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T05:03:26Z |
| publishDate | 2020 |
| publisher | Nanyang Technological University |
| record_format | dspace |
| spelling | ntu-10356/1398152023-02-28T23:43:34Z Computability theory and degree structures Yuan, Bowen Wu Guohua School of Physical and Mathematical Sciences guohua@ntu.edu.sg Science::Mathematics This thesis mainly studies the thin-free degrees. We show the technique to construct a thin-free degree, and construct a hyperimmune-free minimal thin-free degrees below 0'', and a nonbranching thin-free r.e. degree. We also show that any 1-generic degree below 0' is not thin-free, while any nonzero degree below a 2-generic degree is thin-free. Doctor of Philosophy 2020-05-21T12:45:42Z 2020-05-21T12:45:42Z 2020 Thesis-Doctor of Philosophy Yuan, B. (2020). Computability theory and degree structures. Doctoral thesis, Nanyang Technological University, Singapore. https://hdl.handle.net/10356/139815 10.32657/10356/139815 en This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). application/pdf Nanyang Technological University |
| spellingShingle | Science::Mathematics Yuan, Bowen Computability theory and degree structures |
| title | Computability theory and degree structures |
| title_full | Computability theory and degree structures |
| title_fullStr | Computability theory and degree structures |
| title_full_unstemmed | Computability theory and degree structures |
| title_short | Computability theory and degree structures |
| title_sort | computability theory and degree structures |
| topic | Science::Mathematics |
| url | https://hdl.handle.net/10356/139815 |
| work_keys_str_mv | AT yuanbowen computabilitytheoryanddegreestructures |