17 found
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Liang Yu [19]Liangzao Yu [2]
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Profile: Liangyu Yu
  1.  82
    Bjørn Kjos-Hanssen, André Nies, Frank Stephan & Liang Yu (2010). Higher Kurtz Randomness. Annals of Pure and Applied Logic 161 (10):1280-1290.
    A real x is -Kurtz random if it is in no closed null set . We show that there is a cone of -Kurtz random hyperdegrees. We characterize lowness for -Kurtz randomness as being -dominated and -semi-traceable.
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  2.  45
    Rod Downey, Andre Nies, Rebecca Weber & Liang Yu (2006). Lowness and Π₂⁰ Nullsets. Journal of Symbolic Logic 71 (3):1044-1052.
    We prove that there exists a noncomputable c.e. real which is low for weak 2-randomness, a definition of randomness due to Kurtz, and that all reals which are low for weak 2-randomness are low for Martin-Löf randomness.
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  3.  4
    Liang Yu (2006). Lowness for Genericity. Archive for Mathematical Logic 45 (2):233-238.
    We study lowness for genericity. We show that there exists no Turing degree which is low for 1-genericity and all of computably traceable degrees are low for weak 1-genericity.
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  4.  13
    Rod Downey & Liang Yu (2006). Arithmetical Sacks Forcing. Archive for Mathematical Logic 45 (6):715-720.
    We answer a question of Jockusch by constructing a hyperimmune-free minimal degree below a 1-generic one. To do this we introduce a new forcing notion called arithmetical Sacks forcing. Some other applications are presented.
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  5.  13
    Yun Fan & Liang Yu (2011). Maximal Pairs of Ce Reals in the Computably Lipschitz Degrees. Annals of Pure and Applied Logic 162 (5):357-366.
    Computably Lipschitz reducibility , was suggested as a measure of relative randomness. We say α≤clβ if α is Turing reducible to β with oracle use on x bounded by x+c. In this paper, we prove that for any non-computable real, there exists a c.e. real so that no c.e. real can cl-compute both of them. So every non-computable c.e. real is the half of a cl-maximal pair of c.e. reals.
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  6.  2
    Liang Yu & Decheng Ding (2004). There Is No SW-Complete C.E. Real. Journal of Symbolic Logic 69 (4):1163 - 1170.
    We prove that there is no sw-complete c.e. real, negatively answering a question in [6].
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  7.  6
    Liang Yu (2012). Characterizing Strong Randomness Via Martin-Löf Randomness. Annals of Pure and Applied Logic 163 (3):214-224.
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  8.  1
    Liang Yu & Yue Yang (2005). On the Definable Ideal Generated by Nonbounding C.E. Degrees. Journal of Symbolic Logic 70 (1):252 - 270.
    Let [NB]₁ denote the ideal generated by nonbounding c.e. degrees and NCup the ideal of noncuppable c.e. degrees. We show that both [NB]₁ ∪ NCup and the ideal generated by nonbounding and noncuppable degrees are new, in the sense that they are different from M, [NB]₁ and NCup—the only three known definable ideals so far.
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  9.  9
    Liang Yu (2011). A New Proof of Friedman's Conjecture. Bulletin of Symbolic Logic 17 (3):455-461.
    We give a new proof of Friedman's conjecture that every uncountable Δ11 set of reals has a member of each hyperdegree greater than or equal to the hyperjump.
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  10.  14
    Liang Yu & Rod Downey (2004). There Are No Maximal Low D.C.E.~Degrees. Notre Dame Journal of Formal Logic 45 (3):147-159.
    We prove that there is no maximal low d.c.e degree.
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  11. Liang Yu, Decheng Ding & Rodney Downey (2004). The Kolmogorov Complexity of Random Reals. Annals of Pure and Applied Logic 129 (1-3):163-180.
    We investigate the initial segment complexity of random reals. Let K denote prefix-free Kolmogorov complexity. A natural measure of the relative randomness of two reals α and β is to compare complexity K and K. It is well-known that a real α is 1-random iff there is a constant c such that for all n, Kn−c. We ask the question, what else can be said about the initial segment complexity of random reals. Thus, we study the fine behaviour of K (...)
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  12.  11
    Yue Yang & Liang Yu (2006). On Σ₁-Structural Differences Among Finite Levels of the Ershov Hierarchy. Journal of Symbolic Logic 71 (4):1223 - 1236.
    We show that the structure R of recursively enumerable degrees is not a Σ₁-elementary substructure of Dn, where Dn (n > 1) is the structure of n-r.e. degrees in the Ershov hierarchy.
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  13.  5
    Klaus Ambos-Spies, Decheng Ding, Wei Wang & Liang Yu (2009). Bounding Non- GL ₂ and R.E.A. Journal of Symbolic Logic 74 (3):989-1000.
    We prove that every Turing degree a bounding some non-GL₂ degree is recursively enumerable in and above (r.e.a.) some 1-generic degree.
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  14.  4
    Liang Yu (2006). Measure Theory Aspects of Locally Countable Orderings. Journal of Symbolic Logic 71 (3):958 - 968.
    We prove that for any locally countable $\Sigma _{1}^{1}$ partial order P = 〈2ω,≤P〉, there exists a nonmeasurable antichain in P. Some applications of the result are also presented.
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  15.  2
    C. T. Chong & Liang Yu (2007). Maximal Chains in the Turing Degrees. Journal of Symbolic Logic 72 (4):1219 - 1227.
    We study the problem of existence of maximal chains in the Turing degrees. We show that: 1. ZF+DC+"There exists no maximal chain in the Turing degrees" is equiconsistent with ZFC+"There exists an inaccessible cardinal"; 2. For all a ∈ 2ω.(ω₁)L[a] = ω₁ if and only if there exists a $\Pi _{1}^{1}[a]$ maximal chain in the Turing degrees. As a corollary, ZFC + "There exists an inaccessible cardinal" is equiconsistent with ZFC + "There is no (bold face) $\utilde{\Pi}{}_{1}^{1}$ maximal chain of (...)
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  16. C. T. Chong & Liang Yu (2015). Randomness in the Higher Setting. Journal of Symbolic Logic 80 (4):1131-1148.
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  17. Liang Yu (2008). Zheng Ju Xiang Guan Xing Yan Jiu =. Beijing da Xue Chu Ban She.
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