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Jiang Liu [5]Jianguo Liu [1]
  1. Jiang Liu & Guohua Wu (2012). Almost Universal Cupping and Diamond Embeddings. Annals of Pure and Applied Logic 163 (6):717-729.
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  2. Douglas Cenzer, Johanna Ny Franklin, Jiang Liu & Guohua Wu (2011). A Superhigh Diamond in the Ce Tt-Degrees. 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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  3. Jiang Liu & Guohua Wu (2011). An Almost-Universal Cupping Degree. Journal of Symbolic Logic 76 (4):1137-1152.
    Say that an incomplete d.r.e. degree has almost universal cupping property, if it cups all the r.e. degrees not below it to 0′. In this paper, we construct such a degree d, with all the r.e. degrees not cupping d to 0′ bounded by some r.e. degree strictly below d. The construction itself is an interesting 0″′ argument and this new structural property can be used to study final segments of various degree structures in the Ershov hierarchy.
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  4. Jiang Liu, Shenling Wang & Guohua Wu (2010). Infima of D.R.E. Degrees. Archive for Mathematical Logic 49 (1):35-49.
    Lachlan observed that the infimum of two r.e. degrees considered in the r.e. degrees coincides with the one considered in the ${\Delta_2^0}$ degrees. It is not true anymore for the d.r.e. degrees. Kaddah proved in (Ann Pure Appl Log 62(3):207–263, 1993) that there are d.r.e. degrees a, b, c and a 3-r.e. degree x such that a is the infimum of b, c in the d.r.e. degrees, but not in the 3-r.e. degrees, as a < x < b, c. In (...)
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  5. Jiang Liu & Guohua Wu (2010). Joining to High Degrees Via Noncuppables. Archive for Mathematical Logic 49 (2):195-211.
    Cholak, Groszek and Slaman proved in J Symb Log 66:881–901, 2001 that there is a nonzero computably enumerable (c.e.) degree cupping every low c.e. degree to a low c.e. degree. In the same paper, they pointed out that every nonzero c.e. degree can cup a low2 c.e. degree to a nonlow2 degree. In Jockusch et al. (Trans Am Math Soc 356:2557–2568, 2004) improved the latter result by showing that every nonzero c.e. degree c is cuppable to a high c.e. degree (...)
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  6. Jianguo Liu, Dawn Thorndike Pysarchik & William W. Taylor (2002). Peer Review in the Classroom. BioScience 52 (9):824.
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