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  1.  51
    Isolation and the high/low hierarchy.Shamil Ishmukhametov & Guohua Wu - 2002 - 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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  2.  57
    Anti-Complex Sets and Reducibilities with Tiny Use.Johanna N. Y. Franklin, Noam Greenberg, Frank Stephan & Guohua Wu - 2013 - Journal of Symbolic Logic 78 (4):1307-1327.
  3.  16
    Isolation and the Jump Operator.Guohua Wu - 2001 - Mathematical Logic Quarterly 47 (4):525-534.
    We show the existence of a high d. c. e. degree d and a low2 c.e. degree a such that d is isolated by a.
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  4.  59
    On the complexity of the successivity relation in computable linear orderings.Rod Downey, Steffen Lempp & Guohua Wu - 2010 - Journal of Mathematical Logic 10 (1):83-99.
    In this paper, we solve a long-standing open question, about the spectrum of the successivity relation on a computable linear ordering. We show that if a computable linear ordering [Formula: see text] has infinitely many successivities, then the spectrum of the successivity relation is closed upwards in the computably enumerable Turing degrees. To do this, we use a new method of constructing [Formula: see text]-isomorphisms, which has already found other applications such as Downey, Kastermans and Lempp [9] and is of (...)
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  5.  64
    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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  6.  22
    The members of thin and minimal Π 1 0 classes, their ranks and Turing degrees.Rodney G. Downey, Guohua Wu & Yue Yang - 2015 - Annals of Pure and Applied Logic 166 (7-8):755-766.
  7.  64
    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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  8.  19
    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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  9.  56
    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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  10.  22
    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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  11.  49
    Corrigendum: "On the complexity of the successivity relation in computable linear orderings".Rodney G. Downey, Steffen Lempp & Guohua Wu - 2017 - Journal of Mathematical Logic 17 (2):1792002.
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  12.  30
    Degrees containing members of thin Π10 classes are dense and co-dense.Rodney G. Downey, Guohua Wu & Yue Yang - 2018 - Journal of Mathematical Logic 18 (1):1850001.
    In [Countable thin [Formula: see text] classes, Ann. Pure Appl. Logic 59 79–139], Cenzer, Downey, Jockusch and Shore proved the density of degrees containing members of countable thin [Formula: see text] classes. In the same paper, Cenzer et al. also proved the existence of degrees containing no members of thin [Formula: see text] classes. We will prove in this paper that the c.e. degrees containing no members of thin [Formula: see text] classes are dense in the c.e. degrees. We will (...)
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  13.  38
    Degrees of d. c. e. reals.Rod Downey, Guohua Wu & Xizhong Zheng - 2004 - 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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  14.  10
    Highness and local noncappability.Chengling Fang, Wang Shenling & Guohua Wu - 2012 - In S. Barry Cooper (ed.), How the World Computes. pp. 203--211.
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  15.  29
    On a problem of Ishmukhametov.Chengling Fang, Guohua Wu & Mars Yamaleev - 2013 - 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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  16.  14
    Computable linear orders and products.Andrey N. Frolov, Steffen Lempp, Keng Meng Ng & Guohua Wu - 2020 - Journal of Symbolic Logic 85 (2):605-623.
    We characterize the linear order types $\tau $ with the property that given any countable linear order $\mathcal {L}$, $\tau \cdot \mathcal {L}$ is a computable linear order iff $\mathcal {L}$ is a computable linear order, as exactly the finite nonempty order types.
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  17.  15
    Cupping and Jump Classes in the Computably Enumerable Degrees.Noam Greenberg, Keng Meng Ng & Guohua Wu - 2020 - Journal of Symbolic Logic 85 (4):1499-1545.
    We show that there is a cuppable c.e. degree, all of whose cupping partners are high. In particular, not all cuppable degrees are${\operatorname {\mathrm {low}}}_3$-cuppable, or indeed${\operatorname {\mathrm {low}}}_n$cuppable for anyn, refuting a conjecture by Li. On the other hand, we show that one cannot improve highness to superhighness. We also show that the${\operatorname {\mathrm {low}}}_2$-cuppable degrees coincide with the array computable-cuppable degrees, giving a full understanding of the latter class.
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  18.  59
    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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  19.  30
    Jump Operator and Yates Degrees.Guohua Wu - 2006 - 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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  20.  19
    The Kierstead's Conjecture and limitwise monotonic functions.Guohua Wu & Maxim Zubkov - 2018 - Annals of Pure and Applied Logic 169 (6):467-486.
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  21.  17
    Rudin's Lemma and Reverse Mathematics.Gaolin Li, Junren Ru & Guohua Wu - 2017 - Annals of the Japan Association for Philosophy of Science 25:57-66.
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  22.  52
    An almost-universal cupping degree.Jiang Liu & Guohua Wu - 2011 - 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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  23.  11
    Almost universal cupping and diamond embeddings.Jiang Liu & Guohua Wu - 2012 - Annals of Pure and Applied Logic 163 (6):717-729.
  24.  56
    Infima of d.r.e. degrees.Jiang Liu, Shenling Wang & Guohua Wu - 2010 - 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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  25.  50
    Joining to high degrees via noncuppables.Jiang Liu & Guohua Wu - 2010 - 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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  26.  22
    Highness, locally noncappability and nonboundings.Frank Stephan & Guohua Wu - 2013 - 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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  27.  16
    1-Generic splittings of computably enumerable degrees.Guohua Wu - 2006 - 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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  28.  54
    Intervals containing exactly one c.e. degree.Guohua Wu - 2007 - 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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  29.  44
    Q -measures on Q κ λ.Guohua Wu - 2003 - 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.
    No categories
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  30.  30
    Quasi-complements of the cappable degrees.Guohua Wu - 2004 - Mathematical Logic Quarterly 50 (2):189.
    Say that a nonzero c. e. degree b is a quasi-complement of a c. e. degree a if a ∩ b = 0 and a ∪ b is high. It is well-known that each cappable degree has a high quasi-complement. However, by the existence of the almost deep degrees, there are nonzero cappable degrees having no low quasi-complements. In this paper, we prove that any nonzero cappable degree has a low2 quasi-complement.
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  31.  25
    Regular reals.Guohua Wu - 2005 - 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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