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The Low Splitting Theorem in the Difference Hierarchy

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New Computational Paradigms (CiE 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3526))

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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 x 0, x 1 such that both l ≤ x 0, x 1 < a and x 0 ∨ x 1 = a hold, extending the Robinson low splitting theorem for the computably enumerable degrees to the difference hierarchy.

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Author information

Authors and Affiliations

  1. Institute of Software, Chinese Academy of Sciences, Beijing, 100080, P. R. China

    Angsheng Li

Authors
  1. Angsheng Li
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Editor information

Editors and Affiliations

  1. School of Mathematics, University of Leeds, LS2 9JT, Leeds, U.K.

    S. Barry Cooper

  2. Department Mathematik, Universität Hamburg, Bundesstrasse 55, 20146, Hamburg, Germany

    Benedikt Löwe

  3. Universiteit van Amsterdam,  

    Leen Torenvliet

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© 2005 Springer-Verlag Berlin Heidelberg

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Li, A. (2005). The Low Splitting Theorem in the Difference Hierarchy. In: Cooper, S.B., Löwe, B., Torenvliet, L. (eds) New Computational Paradigms. CiE 2005. Lecture Notes in Computer Science, vol 3526. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11494645_35

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  • DOI: https://doi.org/10.1007/11494645_35

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-26179-7

  • Online ISBN: 978-3-540-32266-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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