Nonhemimaximal degrees and the high/low hierarchy
After showing the downwards density of nonhemimaximal degrees, Downey and Stob continued to prove that the existence of a low₂, but not low, nonhemimaximal degree, and their proof uses the fact that incomplete m-topped degrees are low₂ but not low. As commented in their paper, the construction of su...
Saved in:
| Main Authors: | , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
2013
|
| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/99244 http://hdl.handle.net/10220/17146 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Institution: | Nanyang Technological University |
| Language: | English |
| id |
sg-ntu-dr.10356-99244 |
|---|---|
| record_format |
dspace |
| spelling |
sg-ntu-dr.10356-992442020-03-07T12:31:32Z Nonhemimaximal degrees and the high/low hierarchy Fang, Chengling Wu, Guohua School of Physical and Mathematical Sciences DRNTU::Science::Mathematics::Mathematical logic After showing the downwards density of nonhemimaximal degrees, Downey and Stob continued to prove that the existence of a low₂, but not low, nonhemimaximal degree, and their proof uses the fact that incomplete m-topped degrees are low₂ but not low. As commented in their paper, the construction of such a nonhemimaximal degree is actually a primitive 0''' argument. In this paper, we give another construction of such degrees, which is a standard 0''-argument, much simpler than Downey and Stob's construction mentioned above. 2013-10-31T07:20:38Z 2019-12-06T20:05:00Z 2013-10-31T07:20:38Z 2019-12-06T20:05:00Z 2012 2012 Journal Article Fang, C., & Wu, G. (2012). Nonhemimaximal degrees and the high/low hierarchy. Journal of symbolic logic, 77(2), 433-446. 0022-4812 https://hdl.handle.net/10356/99244 http://hdl.handle.net/10220/17146 10.2178/jsl/1333566631 en Journal of symbolic logic |
| institution |
Nanyang Technological University |
| building |
NTU Library |
| country |
Singapore |
| collection |
DR-NTU |
| language |
English |
| topic |
DRNTU::Science::Mathematics::Mathematical logic |
| spellingShingle |
DRNTU::Science::Mathematics::Mathematical logic Fang, Chengling Wu, Guohua Nonhemimaximal degrees and the high/low hierarchy |
| description |
After showing the downwards density of nonhemimaximal degrees, Downey and Stob continued to prove that the existence of a low₂, but not low, nonhemimaximal degree, and their proof uses the fact that incomplete m-topped degrees are low₂ but not low. As commented in their paper, the construction of such a nonhemimaximal degree is actually a primitive 0''' argument. In this paper, we give another construction of such degrees, which is a standard 0''-argument, much simpler than Downey and Stob's construction mentioned above. |
| author2 |
School of Physical and Mathematical Sciences |
| author_facet |
School of Physical and Mathematical Sciences Fang, Chengling Wu, Guohua |
| format |
Article |
| author |
Fang, Chengling Wu, Guohua |
| author_sort |
Fang, Chengling |
| title |
Nonhemimaximal degrees and the high/low hierarchy |
| title_short |
Nonhemimaximal degrees and the high/low hierarchy |
| title_full |
Nonhemimaximal degrees and the high/low hierarchy |
| title_fullStr |
Nonhemimaximal degrees and the high/low hierarchy |
| title_full_unstemmed |
Nonhemimaximal degrees and the high/low hierarchy |
| title_sort |
nonhemimaximal degrees and the high/low hierarchy |
| publishDate |
2013 |
| url |
https://hdl.handle.net/10356/99244 http://hdl.handle.net/10220/17146 |
| _version_ |
1681038194427035648 |