Infima of d.r.e. Degrees

  • Authors:

  • Jiang Liu;Shengling Wang;Guohua Wu

  • Affiliations:

  • Division of Mathematical Sciences School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore 637371;Division of Mathematical Sciences School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore 637371;Division of Mathematical Sciences School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore 637371

  • Venue:
  • CiE '09 Proceedings of the 5th Conference on Computability in Europe: Mathematical Theory and Computational Practice
  • Year:
  • 2009

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Abstract

Lachlan observed that the infimum of two r.e. degrees considered in the r.e. degres coincides with the one considered in the $\Delta_2^0$ degrees. It is not true anymore for the d.r.e. degrees. Kaddah proved in [7] that there are d .r .e . degrees a, b, c and a 3-r .e . degree x such that a is the infimum of b, c in the d.r.e. degrees, but not in the 3-r.e. degrees, as a x b, c. In this paper, we extend Kaddah's result by showing that such a infima difference occurs densely in the r.e. degrees.