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On a Question of Sacks — A Partial Solution on the Positive Side

  • Andrew E. M. Lewis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3526)

Abstract

Let us say that a c.e. operator E is degree invariant on any given Turing degree a if X,YaE(X) ≡  T E(Y) . In [4] we construct a c.e. operator E such that ∀X [ X <  T E(X) <  T X′] . While we are unable to produce degree invariance everywhere, we are able to ensure that for every degree a there exists b such that a ∨ 0′ = b ∨ 0′ and E is degree invariant on b . What appears here is an abbreviated version of the material from that paper, stopping short of most technical details.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Andrew E. M. Lewis
    • 1
  1. 1.University of LeedsLeedsEngland

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