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Weak density and cupping in the d-r.e. degrees

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Abstract

Consider the Turing degrees of differences of recursively enumerable sets (the d-r.e. degrees). We show that there is a properly d-r.e. degree (a d-r.e. degree that is not r.e.) between any two comparable r.e. degrees, and that given a high r.e. degreeh, every nonrecursive d-r.e. degree ≦h cups toh by a low d-r.e. degree.

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Author notes

  1. Steffen Lempp

    Present address: Department of Mathematics, University of Wisconsin, 53706, Madison, WI, USA

  2. Philip Watson

    Present address: Department of Computer Science, University of London, Royal Holloway and Bedford New 0664 College, Egham Hill, Egham, TW20 0EX, Surrey, England

Authors and Affiliations

  1. School of Mathematics, University of Leeds, LS2 9JT, Leeds, England

    S. Barry Cooper & Philip Watson

  2. Department of Mathematics, Yale University, 06520, New Haven, CT, USA

    Steffen Lempp

Authors
  1. S. Barry Cooper
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  2. Steffen Lempp
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  3. Philip Watson
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Additional information

The second author was partially supported by NSF grant DMS-8701891.

The third author was supported by an SEFC research grant.

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Cooper, S.B., Lempp, S. & Watson, P. Weak density and cupping in the d-r.e. degrees. Israel J. Math. 67, 137–152 (1989). https://doi.org/10.1007/BF02937291

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  • DOI: https://doi.org/10.1007/BF02937291

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