Cupping $\Delta_2^0$ Enumeration Degrees to 0e'

  • Authors:

  • Mariya Ivanova Soskova;Guohua Wu

  • Affiliations:

  • Department of Pure Mathematics, University of Leeds, Leeds LS2 9JT, U.K.;School of Physical and Mathematical Sciences, Nanyang Technological University, 639798, Singapore

  • Venue:
  • CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
  • Year:
  • 2007

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Abstract

In this paper we prove that every nonzero $\Delta^0_2$e-degree is cuppable to 0e' bya 1-generic $\Delta^0_2$ e-degree (so low and nontotal)and that every nonzero ω-c.e. e-degree is cuppableto 0e' by an incomplete 3-c.e.e-degree.