The low splitting theorem in the difference hierarchy

  • Authors:

  • Angsheng Li

  • Affiliations:

  • Institute of Software, Chinese Academy of Sciences, Beijing, P. R. China

  • Venue:
  • CiE'05 Proceedings of the First international conference on Computability in Europe: new Computational Paradigms
  • Year:
  • 2005

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Abstract

It is shown that for any 2-computably enumerable Turing degrees a, l, if l ′ = 0′, and l a, then there are 2-computably enumerable Turing degrees x0, x1 such that both l ≤ x0, x1 a and x0 ∨ x1 = a hold, extending the Robinson low splitting theorem for the computably enumerable degrees to the difference hierarchy.