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  1. 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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  • An extended Lachlan splitting theorem.Steffen Lempp & Sui Yuefei - 1996 - Annals of Pure and Applied Logic 79 (1):53-59.
    We show that the top of any diamond with bottom 0 in the r.e. degrees is also the top of a stack of n diamonds with bottom 0.
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  • Infima in the Recursively Enumerable Weak Truth Table Degrees.Rich Blaylock, Rod Downey & Steffen Lempp - 1997 - Notre Dame Journal of Formal Logic 38 (3):406-418.
    We show that for every nontrivial r.e. wtt-degree a, there are r.e. wtt-degrees b and c incomparable to a such that the infimum of a and b exists but the infimum of a and c fails to exist. This shows in particular that there are no strongly noncappable r.e. wtt-degrees, in contrast to the situation in the r.e. Turing degrees.
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  • Intervals and sublattices of the R.E. weak truth table degrees, part I: Density.R. G. Downey - 1989 - Annals of Pure and Applied Logic 41 (1):1-26.
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  • Bezem, M., see Barendsen, E.G. M. Bierman, M. DZamonja, S. Shelah, S. Feferman, G. Jiiger, M. A. Jahn, S. Lempp, Sui Yuefei, S. D. Leonhardi & D. Macpherson - 1996 - Annals of Pure and Applied Logic 79 (1):317.
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  • Embeddings of N5 and the contiguous degrees.Klaus Ambos-Spies & Peter A. Fejer - 2001 - Annals of Pure and Applied Logic 112 (2-3):151-188.
    Downey and Lempp 1215–1240) have shown that the contiguous computably enumerable degrees, i.e. the c.e. Turing degrees containing only one c.e. weak truth-table degree, can be characterized by a local distributivity property. Here we extend their result by showing that a c.e. degree a is noncontiguous if and only if there is an embedding of the nonmodular 5-element lattice N5 into the c.e. degrees which maps the top to the degree a. In particular, this shows that local nondistributivity coincides with (...)
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  • Continuity of capping in C bT.Paul Brodhead, Angsheng Li & Weilin Li - 2008 - Annals of Pure and Applied Logic 155 (1):1-15.
    A set Asubset of or equal toω is called computably enumerable , if there is an algorithm to enumerate the elements of it. For sets A,Bsubset of or equal toω, we say that A is bounded Turing reducible to reducible to) B if there is a Turing functional, Φ say, with a computable bound of oracle query bits such that A is computed by Φ equipped with an oracle B, written image. Let image be the structure of the c.e. bT-degrees, (...)
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  • Classifications of degree classes associated with r.e. subspaces.R. G. Downey & J. B. Remmel - 1989 - Annals of Pure and Applied Logic 42 (2):105-124.
    In this article we show that it is possible to completely classify the degrees of r.e. bases of r.e. vector spaces in terms of weak truth table degrees. The ideas extend to classify the degrees of complements and splittings. Several ramifications of the classification are discussed, together with an analysis of the structure of the degrees of pairs of r.e. summands of r.e. spaces.
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  • (1 other version)A Contiguous Nonbranching Degree.Rod Downey - 1989 - Mathematical Logic Quarterly 35 (4):375-383.
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  • Structural interactions of the recursively enumerable T- and W-degrees.R. G. Downey & M. Stob - 1986 - Annals of Pure and Applied Logic 31:205-236.
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  • The discontinuity of splitting in the recursively enumerable degrees.S. Barry Cooper & Xiaoding Yi - 1995 - Archive for Mathematical Logic 34 (4):247-256.
    In this paper we examine a class of pairs of recursively enumerable degrees, which is related to the Slaman-Soare Phenomenon.
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  • The recursively enumerable degrees have infinitely many one-types.Klaus Ambos-Spies & Robert I. Soare - 1989 - Annals of Pure and Applied Logic 44 (1-2):1-23.
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  • Anti‐Mitotic Recursively Enumerable Sets.Klaus Ambos-Spies - 1985 - Mathematical Logic Quarterly 31 (29-30):461-477.
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