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On very high degrees

Journal of Symbolic Logic 73 (1):309-342 (2008)

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  1. Bounded-low sets and the high/low hierarchy.Huishan Wu - 2020 - Archive for Mathematical Logic 59 (7-8):925-938.
    Anderson and Csima defined a bounded jump operator for bounded-Turing reduction, and studied its basic properties. Anderson et al. constructed a low bounded-high set and conjectured that such sets cannot be computably enumerable. Ng and Yu proved that bounded-high c.e. sets are Turing complete, thus answered the conjecture positively. Wu and Wu showed that bounded-low sets can be superhigh by constructing a Turing complete bounded-low c.e. set. In this paper, we continue the study of the comparison between the bounded-jump and (...)
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  • Strong Jump-Traceability.Noam Greenberg & Dan Turetsky - 2018 - Bulletin of Symbolic Logic 24 (2):147-164.
    We review the current knowledge concerning strong jump-traceability. We cover the known results relating strong jump-traceability to randomness, and those relating it to degree theory. We also discuss the techniques used in working with strongly jump-traceable sets. We end with a section of open questions.
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  • Splitting into degrees with low computational strength.Rod Downey & Keng Meng Ng - 2018 - Annals of Pure and Applied Logic 169 (8):803-834.
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  • A superhigh diamond in the c.e. tt-degrees.Douglas Cenzer, Johanna Ny Franklin, Jiang Liu & Guohua Wu - 2011 - Archive for Mathematical Logic 50 (1-2):33-44.
    The notion of superhigh computably enumerable (c.e.) degrees was first introduced by (Mohrherr in Z Math Logik Grundlag Math 32: 5–12, 1986) where she proved the existence of incomplete superhigh c.e. degrees, and high, but not superhigh, c.e. degrees. Recent research shows that the notion of superhighness is closely related to algorithmic randomness and effective measure theory. Jockusch and Mohrherr proved in (Proc Amer Math Soc 94:123–128, 1985) that the diamond lattice can be embedded into the c.e. tt-degrees preserving 0 (...)
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