Joining to High Degrees

  • Jiang Liu
  • Guohua Wu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5028)


Cholak, Groszek and Slaman proved in [1] that there is a nonzero computably enumerable (c.e.) degree cupping every low c.e. degree to a low c.e. degree. In the same paper, they pointed out that every nonzero c.e. degree can cup a low2 c.e. degree to a nonlow2 degree. In [2], Jockusch, Li and Yang improved the latter result by showing that every nonzero c.e. degree c is cuppable to a high c.e. degree by a low2 c.e. degree b. It is natural to ask in which subclass of low2 c.e. degrees b in [2] can be located. Wu proved [6] that b can be cappable. We prove in this paper that b in Jockusch, Li and Yang’s result can be noncuppable, improving both Jockusch, Li and Yang, and Wu’s results.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Jiang Liu
    • 1
  • Guohua Wu
    • 1
  1. 1.School of Physical and Mathematical SciencesNanyang Technological UniversitySingapore

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