Nonhemimaximal degrees and the high/low hierarchy
Chengling Fang and Guohua Wu
Source: J. Symbolic Logic Volume 77, Issue 2
(2012), 433-446.
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.
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