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...
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Nanyang Technological University
2020
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| Online Access: | https://hdl.handle.net/10356/139815 |
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sg-ntu-dr.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 |
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Science::Mathematics Yuan, Bowen Computability theory and degree structures |
| 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. |
| author2 |
Wu Guohua |
| author_facet |
Wu Guohua Yuan, Bowen |
| format |
Thesis-Doctor of Philosophy |
| author |
Yuan, Bowen |
| author_sort |
Yuan, Bowen |
| title |
Computability theory and degree structures |
| title_short |
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_sort |
computability theory and degree structures |
| publisher |
Nanyang Technological University |
| publishDate |
2020 |
| url |
https://hdl.handle.net/10356/139815 |
| _version_ |
1759855266711470080 |