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...
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| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
2013
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/99244 http://hdl.handle.net/10220/17146 |
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| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | 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. |
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