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Finite cupping sets

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Abstract.

We show that given any (Turing) degree 0<c≤0’ and any uniformly Δ2 sequence of degrees b 0 ,b 1 ,b 2 ,.. such that ∀i(b i ≱ c), there exists 0<a<0’ such that for all i≥0, a∨b i ≱ c. If c is c.e. and b 0 ,b 1 ,b 2 ,.. are uniformly (strictly) below c then there exists such an a below c.

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References

  1. Lewis, A.: Minimal Complements For Degrees Below 0’, Jan 02, unpublished

  2. Lewis, A.: A Single Minimal Complement For The C.E. Degrees, Apr 02, unpublished

  3. Li, A., Yi, X.: Cupping the recursively enumerable degrees by d.r.e. degrees, Proc. London Math. Soc. 79 (3) , 1–21 (1999)

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  4. Posner, Robinson, Degrees Joining to 0’, 1981 J. Symbolic Logic 46, 714–722 (1981)

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Authors and Affiliations

  1. Department of Mathematics, Leeds University, Leeds, England

    Andrew Lewis

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  1. Andrew Lewis
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Correspondence to Andrew Lewis.

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Lewis, A. Finite cupping sets. Arch. Math. Logic 43, 845–858 (2004). https://doi.org/10.1007/s00153-004-0215-5

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  • DOI: https://doi.org/10.1007/s00153-004-0215-5

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