Classifying C.E. Sets

  • Robert I. Soare
Chapter
Part of the Theory and Applications of Computability book series (THEOAPPLCOM)

Abstract

In §1.6 we constructed a noncomputable c.e. set K. In §2.4 we studied creative sets and showed that all are computably isomorphic to K. So far the noncomputable c.e. sets we have exhibited are all computably isomorphic to K and therefore of Turing degree 0′. Post in [Post 1944] asked whether there is only one noncomputable c.e. set up to Turing equivalence.

Keywords

Computable Function Computable Enumeration Turing Degree Nonzero Degree Turing Reduction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Robert I. Soare
    • 1
  1. 1.Department of MathematicsThe University of ChicagoChicagoUSA

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