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  1. Contiguity and Distributivity in the Enumerable Turing Degrees.Rodney G. Downey & Steffen Lempp - 1997 - Journal of Symbolic Logic 62 (4):1215-1240.
    We prove that a enumerable degree is contiguous iff it is locally distributive. This settles a twenty-year old question going back to Ladner and Sasso. We also prove that strong contiguity and contiguity coincide, settling a question of the first author, and prove that no $m$-topped degree is contiguous, settling a question of the first author and Carl Jockusch [11]. Finally, we prove some results concerning local distributivity and relativized weak truth table reducibility.
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  • Lattice embeddings and array noncomputable degrees.Stephen M. Walk - 2004 - Mathematical Logic Quarterly 50 (3):219.
    We focus on a particular class of computably enumerable degrees, the array noncomputable degrees defined by Downey, Jockusch, and Stob, to answer questions related to lattice embeddings and definability in the partial ordering of c. e. degrees under Turing reducibility. We demonstrate that the latticeM5 cannot be embedded into the c. e. degrees below every array noncomputable degree, or even below every nonlow array noncomputable degree. As Downey and Shore have proved that M5 can be embedded below every nonlow2 degree, (...)
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