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On the distribution of Lachlan nonsplitting bases

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Abstract.

 We say that a computably enumerable (c.e.) degree b is a Lachlan nonsplitting base (LNB), if there is a computably enumerable degree a such that a > b, and for any c.e. degrees w,v ≤ a, if a ≤ w or; v or; b then either a ≤ w or; b or a ≤ v or; b. In this paper we investigate the relationship between bounding and nonbounding of Lachlan nonsplitting bases and the high /low hierarchy. We prove that there is a non-Low2 c.e. degree which bounds no Lachlan nonsplitting base.

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Authors and Affiliations

  1. School of Mathematics, University of Leeds, Leeds LS2 9JT, UK. e-mail: s.b.cooper@leeds.ac.uk, , , , , , GB

    S. Barry Cooper

  2. School of Mathematics, University of Leeds, Leeds LS2 9JT, UK. e-mail: angsheng@amsta.leeds.ac.uk. Permanent address: Institute of Software, Academia Sinica, P.O. Box 8718, Beijing, P. R. China. e-mail: angsheng@ios.ac.cn, , , , , , CN

    Angsheng Li

  3. Department of Computer Science, University of British Columbia, Vancouver, B.C. Canada V6T 1Z4. e-mail: yi@cs.ubc.ca, , , , , , CA

    Xiaoding Yi

Authors
  1. S. Barry Cooper
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  2. Angsheng Li
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  3. Xiaoding Yi
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Received: 11 October 1999 / Published online: 7 May 2002

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Cooper, S., Li, A. & Yi, X. On the distribution of Lachlan nonsplitting bases. Arch. Math. Logic 41, 455–482 (2002). https://doi.org/10.1007/s001530100095

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  • DOI: https://doi.org/10.1007/s001530100095

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