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  1. Chengling Fang, Guohua Wu & Mars Yamaleev (2013). On a Problem of Ishmukhametov. Archive for Mathematical Logic 52 (7-8):733-741.
    Given a d.c.e. degree d, consider the d.c.e. sets in d and the corresponding degrees of their Lachlan sets. Ishmukhametov provided a systematic investigation of such degrees, and proved that for a given d.c.e. degree d > 0, the class of its c.e. predecessors in which d is c.e., denoted as R[d], can consist of either just one element, or an interval of c.e. degrees. After this, Ishmukhametov asked whether there exists a d.c.e. degree d for which the class R[d] (...)
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  2. Frank Stephan & Guohua Wu (2013). Highness, Locally Noncappability and Nonboundings. Annals of Pure and Applied Logic 164 (5):511-522.
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  3. Chengling Fang, Wang Shenling & Guohua Wu (2012). Highness and Local Noncappability. In S. Barry Cooper (ed.), How the World Computes. 203--211.
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  4. Chengling Fang & Guohua Wu (2012). Nonhemimaximal Degrees and the High/Low Hierarchy. Journal of Symbolic Logic 77 (2):433-446.
    After showing the downwards density of nonhemimaximal degrees, Downey and Stob continued to prove that the existence of a low₂, but not low, nonhemimaximal degree, and their proof uses the fact that incomplete m-topped degrees are low₂ but not low. As commented in their paper, the construction of such a nonhemimaximal degree is actually a primitive 0''' argument. In this paper, we give another construction of such degrees, which is a standard 0''-argument, much simpler than Downey and Stob's construction mentioned (...)
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  5. 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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  6. 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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  7. 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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  8. Rod Downey, Steffen Lempp & Guohua Wu (2010). On the Complexity of the Successivity Relation in Computable Linear Orderings. Journal of Mathematical Logic 10 (01n02):83-99.
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  9. 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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  10. 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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  11. Guohua Wu (2007). Intervals Containing Exactly One Ce Degree. Annals of Pure and Applied Logic 146 (1):91-102.
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  12. Angsheng Li, Guohua Wu & Yue Yang (2006). Bounding Computably Enumerable Degrees in the Ershov Hierarchy. Annals of Pure and Applied Logic 141 (1):79-88.
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  13. Guohua Wu (2006). Jump Operator and Yates Degrees. Journal of Symbolic Logic 71 (1):252 - 264.
    In [9]. Yates proved the existence of a Turing degree a such that 0. 0′ are the only c.e. degrees comparable with it. By Slaman and Steel [7], every degree below 0′ has a 1-generic complement, and as a consequence. Yates degrees can be 1-generic, and hence can be low. In this paper, we prove that Yates degrees occur in every jump class.
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  14. Guohua Wu (2006). 1-Generic Splittings of Computably Enumerable Degrees. Annals of Pure and Applied Logic 138 (1):211-219.
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  15. Guohua Wu (2005). Regular Reals. Mathematical Logic Quarterly 51 (2):111-119.
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  16. Rod Downey, Angsheng Li & Guohua Wu (2004). Complementing Cappable Degrees in the Difference Hierarchy. Annals of Pure and Applied Logic 125 (1-3):101-118.
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  17. Rod Downey, Guohua Wu & Xizhong Zheng (2004). Degrees of D. C. E. Reals. Mathematical Logic Quarterly 50 (4‐5):345-350.
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  18. Guohua Wu (2004). Bi-Isolation in the D.C.E. Degrees. 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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  19. Guohua Wu (2003). Q-Measures on Q Κ Λ. Archive for Mathematical Logic 42 (2):201-204.
    We give a characterization of strongly compact cardinals in terms of Q κ λ. We also prove that weakly normal Q-measures on Q κ λ are ⊂κ-normal.
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  20. Guohua Wu (2003). Q-Measures on Q [Sub Κ] Λ. Archive for Mathematical Logic 42 (2).
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  21. Shamil Ishmukhametov & Guohua Wu (2002). Isolation and the High/Low Hierarchy. Archive for Mathematical Logic 41 (3):259-266.
    Say that a d.c.e. degree d is isolated by a c.e. degree b, if bMathematics Subject Classification (2000): 03D25, 03D30, 03D35 RID=""ID="" Key words or phrases: Computably enumerable (...)
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  22. Guohua Wu (2002). Isolation and Lattice Embeddings. 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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  23. Guohua Wu (2002). Nonisolated Degrees and the Jump Operator. Annals of Pure and Applied Logic 117 (1-3):209-221.
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