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  1. A limit on relative genericity in the recursively enumerable sets.Steffen Lempp & Theodore A. Slaman - 1989 - Journal of Symbolic Logic 54 (2):376-395.
    Work in the setting of the recursively enumerable sets and their Turing degrees. A set X is low if X', its Turning jump, is recursive in $\varnothing'$ and high if X' computes $\varnothing''$ . Attempting to find a property between being low and being recursive, Bickford and Mills produced the following definition. W is deep, if for each recursively enumerable set A, the jump of $A \bigoplus W$ is recursive in the jump of A. We prove that there are no (...)
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  • A jump class of noncappable degrees.S. B. Cooper - 1989 - Journal of Symbolic Logic 54 (2):324-353.
  • Maximal contiguous degrees.Peter Cholak, Rod Downey & Stephen Walk - 2002 - Journal of Symbolic Logic 67 (1):409-437.
    A computably enumerable (c.e.) degree is a maximal contiguous degree if it is contiguous and no c.e. degree strictly above it is contiguous. We show that there are infinitely many maximal contiguous degrees. Since the contiguous degrees are definable, the class of maximal contiguous degrees provides the first example of a definable infinite anti-chain in the c.e. degrees. In addition, we show that the class of maximal contiguous degrees forms an automorphism base for the c.e. degrees and therefore for the (...)
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