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  1. Isolation and Lattice Embeddings.Guohua Wu - 2002 - Journal of Symbolic Logic 67 (3):1055-1064.
    Say that (a, d) is an isolation pair if a is a c.e. degree, d is a d.c.e. degree, a < d and a bounds all c.e. degrees below d. We prove that there are an isolation pair (a, d) and a c.e. degree c such that c is incomparable with a, d, and c cups d to o', caps a to o. Thus, {o, c, d, o'} is a diamond embedding, which was first proved by Downey in [9]. Furthermore, (...)
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  • Nonisolated Degrees and the Jump Operator.Guohua Wu - 2002 - Annals of Pure and Applied Logic 117 (1-3):209-221.
    Say that a d.c.e. degree d is nonisolated if for any c.e. degree a
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  • Complementing Cappable Degrees in the Difference Hierarchy.Rod Downey, Angsheng Li & Guohua Wu - 2004 - Annals of Pure and Applied Logic 125 (1-3):101-118.
    We prove that for any computably enumerable degree c, if it is cappable in the computably enumerable degrees, then there is a d.c.e. degree d such that c d = 0′ and c ∩ d = 0. Consequently, a computably enumerable degree is cappable if and only if it can be complemented by a nonzero d.c.e. degree. This gives a new characterization of the cappable degrees.
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  • Bounding Computably Enumerable Degrees in the Ershov Hierarchy.Angsheng Li, Guohua Wu & Yue Yang - 2006 - Annals of Pure and Applied Logic 141 (1):79-88.
    Lachlan observed that any nonzero d.c.e. degree bounds a nonzero c.e. degree. In this paper, we study the c.e. predecessors of d.c.e. degrees, and prove that given a nonzero d.c.e. degree , there is a c.e. degree below and a high d.c.e. degree such that bounds all the c.e. degrees below . This result gives a unified approach to some seemingly unrelated results. In particular, it has the following two known theorems as corollaries: there is a low c.e. degree isolating (...)
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  • The Existence of High Nonbounding Degrees in the Difference Hierarchy.Chi Tat Chong, Angsheng Li & Yue Yang - 2006 - Annals of Pure and Applied Logic 138 (1):31-51.
    We study the jump hierarchy of d.c.e. Turing degrees and show that there exists a high d.c.e. degree d which does not bound any minimal pair of d.c.e. degrees.
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  • Isolation in the CEA Hierarchy.Geoffrey LaForte - 2004 - Archive for Mathematical Logic 44 (2):227-244.
    Examining various kinds of isolation phenomena in the Turing degrees, I show that there are, for every n>0, (n+1)-c.e. sets isolated in the n-CEA degrees by n-c.e. sets below them. For n≥1 such phenomena arise below any computably enumerable degree, and conjecture that this result holds densely in the c.e. degrees as well. Surprisingly, such isolation pairs also exist where the top set has high degree and the isolating set is low, although the complete situation for jump classes remains unknown.
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  • Extending and Interpreting Post’s Programme.S. Barry Cooper - 2010 - Annals of Pure and Applied Logic 161 (6):775-788.
    Computability theory concerns information with a causal–typically algorithmic–structure. As such, it provides a schematic analysis of many naturally occurring situations. Emil Post was the first to focus on the close relationship between information, coded as real numbers, and its algorithmic infrastructure. Having characterised the close connection between the quantifier type of a real and the Turing jump operation, he looked for more subtle ways in which information entails a particular causal context. Specifically, he wanted to find simple relations on reals (...)
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  • Bi-Isolation in the D.C.E. Degrees.Guohua Wu - 2004 - Journal of Symbolic Logic 69 (2):409 - 420.
    In this paper, we study the bi-isolation phenomena in the d.c.e. degrees and prove that there are c.e. degrees c₁ < c₂ and a d.c.e. degree d ∈ (c₁, c₂) such that (c₁, d) and (d, c₂) contain no c.e. degrees. Thus, the c.e. degrees between c₁ and c₂ are all incomparable with d. We also show that there are d.c.e. degrees d₁ < d₂ such that (d₁, d₂) contains a unique c.e. degree.
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  • Bi-Isolation in the D.C.E. Degrees.Guohua Wu - 2004 - Journal of Symbolic Logic 69 (2):409-420.
    In this paper, we study the bi-isolation phenomena in the d.c.e. degrees and prove that there are c.e. degrees c1 < c2 and a d.c.e. degree d∈ such that and contain no c.e. degrees. Thus, the c.e. degrees between c1 and c2 are all incomparable with d. We also show that there are d.c.e. degrees d1 < d2 such that contains a unique c.e. degree.
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