Nonhemimaximal degrees and the high/low hierarchy
Author
Fang, Chengling
Wu, Guohua
Date of Issue
2012School
School of Physical and Mathematical Sciences
Abstract
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.
Subject
DRNTU::Science::Mathematics::Mathematical logic
Type
Journal Article
Series/Journal Title
Journal of symbolic logic
Collections
http://dx.doi.org/10.2178/jsl/1333566631
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