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Nonhemimaximal degrees and the high/low hierarchy

  • Fang Chengling (a1) and Wu Guohua (a1)

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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[10] Soare, R.I., Recursively enumerable sets and degrees, Springer-Verlag, Heidelberg, 1987.
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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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