High Minimal Pairs in the Enumeration Degrees

  • Andrea Sorbi
  • Guohua Wu
  • Yue Yang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5532)


The natural embedding of the Turing degrees into the enumeration degrees preserves the jump operation, and maps isomorphically the computably enumerable Turing degrees onto the \({\it \Pi}^0_1\) enumeration degrees. The embedding does not preserve minimal pairs, though, unless one of the two sides is low. In particular it is known that there exist high minimal pairs of c.e. Turing degrees that do not embed to minimal pairs of e-degrees. We show however that high minimal pairs of \({\it \Pi}^0_1\) e-degrees do exist.


Natural Embedding Minimal Pair Computable Enumeration True Stage True Path 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Andrea Sorbi
    • 1
  • Guohua Wu
    • 2
  • Yue Yang
    • 3
  1. 1.University of SienaSienaItaly
  2. 2.Nanyang Technological UniversitySingapore
  3. 3.National University of SingaporeSingapore

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