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 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.
Permanent link to this document: http://projecteuclid.org/euclid.jsl/1333566631
Digital Object Identifier: doi:10.2178/jsl/1333566631
Zentralblatt MATH identifier: 06047770
Mathematical Reviews number (MathSciNet): MR2963015