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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.
    In this paper, we improve a result of Seetapun and prove that above any nonzero, incomplete recursively enumerable degree a, there is a high2 r.e. degree c>ac>a witnessing that a is locally noncappable . Theorem 1.1 provides a scheme of obtaining high2 nonboundings , as all known high2 nonboundings, such as high2 degrees bounding no minimal pairs, high2 plus-cuppings, etc.
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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.
  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.
  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.
    Cooper proved in [S.B. Cooper, Strong minimal covers for recursively enumerable degrees, Math. Logic Quart. 42 191–196] the existence of a c.e. degree with a strong minimal cover . So is the greastest c.e. degree below . Cooper and Yi pointed out in [S.B. Cooper, X. Yi, Isolated d.r.e. degrees, University of Leeds, Dept. of Pure Math., 1995. Preprint] that this strongly minimal cover cannot be d.c.e., and meanwhile, they proposed the notion of isolated degrees: a d.c.e. degree is isolated (...)
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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.
    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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  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.
    Say a set Gω is 1-generic if for any eω, there is a string σG such that {e}σ↓ or τσ↑). It is known that can be split into two 1-generic degrees. In this paper, we generalize this and prove that any nonzero computably enumerable degree can be split into two 1-generic degrees. As a corollary, no two computably enumerable degrees bound the same class of 1-generic degrees.
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  15. Guohua Wu (2005). Regular Reals. Mathematical Logic Quarterly 51 (2):111-119.
    Say that α is an n-strongly c. e. real if α is a sum of n many strongly c. e. reals, and that α is regular if α is n-strongly c. e. for some n. Let Sn be the set of all n-strongly c. e. reals, Reg be the set of regular reals and CE be the set of c. e. reals. Then we have: S1 ⊂ S2 ⊂ · · · ⊂ Sn ⊂ · · · ⊂ ⊂ Reg (...)
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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.
    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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  17. Rod Downey, Guohua Wu & Xizhong Zheng (2004). Degrees of D. C. E. Reals. Mathematical Logic Quarterly 50 (4‐5):345-350.
    A real α is called a c. e. real if it is the halting probability of a prefix free Turing machine. Equivalently, α is c. e. if it is left computable in the sense that L = {q ∈ ℚ : q ≤ α} is a computably enumerable set. The natural field formed by the c. e. reals turns out to be the field formed by the collection of the d. c. e. reals, which are of the form α—β, where (...)
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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):201-204.
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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.
    Say that a d.c.e. degree d is nonisolated if for any c.e. degree a
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