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Liang Yu [30]Liangzao Yu [2]Liang-Chih Yu [1]
  1.  15
    Lowness for Genericity.Liang Yu - 2006 - 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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  2.  72
    Lowness and Π₂⁰ Nullsets.Rod Downey, Andre Nies, Rebecca Weber & Liang Yu - 2006 - 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.  13
    Randomness in the Higher Setting.C. T. Chong & Liang Yu - 2015 - Journal of Symbolic Logic 80 (4):1131-1148.
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  4.  28
    A New Proof of Friedman's Conjecture.Liang Yu - 2011 - 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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  5.  18
    There Is No SW-Complete C.E. Real.Liang Yu & Decheng Ding - 2004 - 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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  6.  25
    The Kolmogorov Complexity of Random Reals.Liang Yu, Decheng Ding & Rodney Downey - 2004 - 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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  7.  43
    Bounding Non- GL ₂ and R.E.A.Klaus Ambos-Spies, Decheng Ding, Wei Wang & Liang Yu - 2009 - 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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  8. Higher Kurtz Randomness.Bjørn Kjos-Hanssen, André Nies, Frank Stephan & Liang Yu - 2010 - 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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  9.  32
    On the Definable Ideal Generated by Nonbounding C.E. Degrees.Liang Yu & Yue Yang - 2005 - 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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  10.  16
    Characterizing Strong Randomness Via Martin-Löf Randomness.Liang Yu - 2012 - Annals of Pure and Applied Logic 163 (3):214-224.
  11.  27
    On Σ₁-Structural Differences Among Finite Levels of the Ershov Hierarchy.Yue Yang & Liang Yu - 2006 - 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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  12.  32
    Maximal Pairs of C.E. Reals in the Computably Lipschitz Degrees.Yun Fan & Liang Yu - 2011 - 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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  13. Proceedings of the 14th and 15th Asian Logic Conferences.Byunghan Kim, Jörg Brendle, Gyesik Lee, Fenrong Liu, R. Ramanujam, Shashi M. Srivastava, Akito Tsuboi & Liang Yu (eds.) - 2019
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  14. Luzin’s (N) and Randomness Reflection.Arno Pauly, Linda Westrick & Liang Yu - 2022 - Journal of Symbolic Logic 87 (2):802-828.
    We show that a computable function $f:\mathbb R\rightarrow \mathbb R$ has Luzin’s property if and only if it reflects $\Pi ^1_1$ -randomness, if and only if it reflects $\Delta ^1_1$ -randomness, and if and only if it reflects ${\mathcal {O}}$ -Kurtz randomness, but reflecting Martin–Löf randomness or weak-2-randomness does not suffice. Here a function f is said to reflect a randomness notion R if whenever $f$ is R-random, then x is R-random as well. If additionally f is known to have (...)
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  15. Psychiatric Document Retrieval Using a Discourse-Aware Model.Liang-Chih Yu, Chung-Hsien Wu & Fong-Lin Jang - 2009 - Artificial Intelligence 173 (7-8):817-829.
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  16. Zheng Ju Xiang Guan Xing Yan Jiu =.Liang Yu - 2008 - Beijing da Xue Chu Ban She.
    本书从界定证据相关性的内涵入手,分别探讨了逻辑上的相关性和法律上的相关性,从而澄清了一些在借鉴英美国家证据规则时出现的概念混淆。.
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  17.  15
    Basis Theorems for -Sets.Chi Tat Chong, Liuzhen Wu & Liang Yu - 2019 - Journal of Symbolic Logic 84 (1):376-387.
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  18.  9
    An Application of Recursion Theory to Analysis.Liang Yu - 2020 - Bulletin of Symbolic Logic 26 (1):15-25.
    Mauldin [15] proved that there is an analytic set, which cannot be represented by $B\cup X$ for some Borel set B and a subset X of a $\boldsymbol{\Sigma }^0_2$ -null set, answering a question by Johnson [10]. We reprove Mauldin’s answer by a recursion-theoretical method. We also give a characterization of the Borel generated $\sigma $ -ideals having approximation property under the assumption that every real is constructible, answering Mauldin’s question raised in [15].
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  19.  30
    Arithmetical Sacks Forcing.Rod Downey & Liang Yu - 2006 - 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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  20.  10
    Being Low Along a Sequence and Elsewhere.Wolfgang Merkle & Liang Yu - 2019 - Journal of Symbolic Logic 84 (2):497-516.
    Let an oracle be called low for prefix-free complexity on a set in case access to the oracle improves the prefix-free complexities of the members of the set at most by an additive constant. Let an oracle be called weakly low for prefix-free complexity on a set in case the oracle is low for prefix-free complexity on an infinite subset of the given set. Furthermore, let an oracle be called low and weakly for prefix-free complexity along a sequence in case (...)
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  21.  42
    There Are No Maximal Low D.C.E. Degrees.Liang Yu & Rod Downey - 2004 - Notre Dame Journal of Formal Logic 45 (3):147-159.
  22.  5
    Chaitin’s Ω as a Continuous Function.Rupert Hölzl, Wolfgang Merkle, Joseph Miller, Frank Stephan & Liang Yu - 2020 - Journal of Symbolic Logic 85 (1):486-510.
    We prove that the continuous function${\rm{\hat \Omega }}:2^\omega \to $ that is defined via$X \mapsto \mathop \sum \limits_n 2^{ - K\left} $ for all $X \in {2^\omega }$ is differentiable exactly at the Martin-Löf random reals with the derivative having value 0; that it is nowhere monotonic; and that $\mathop \smallint \nolimits _0^1{\rm{\hat{\Omega }}}\left\,{\rm{d}}X$ is a left-c.e. $wtt$-complete real having effective Hausdorff dimension ${1 / 2}$.We further investigate the algorithmic properties of ${\rm{\hat{\Omega }}}$. For example, we show that the maximal (...)
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  23.  2
    Luzin’s (N) and Randomness Reflection.Arno Pauly, Linda Westrick & Liang Yu - 2020 - Journal of Symbolic Logic:1-27.
    We show that a computable function $f:\mathbb R\rightarrow \mathbb R$ has Luzin’s property if and only if it reflects $\Pi ^1_1$ -randomness, if and only if it reflects $\Delta ^1_1$ -randomness, and if and only if it reflects ${\mathcal {O}}$ -Kurtz randomness, but reflecting Martin–Löf randomness or weak-2-randomness does not suffice. Here a function f is said to reflect a randomness notion R if whenever $f$ is R-random, then x is R-random as well. If additionally f is known to have (...)
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  24.  10
    Maximal Chains in the Turing Degrees.C. T. Chong & Liang Yu - 2007 - 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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  25.  7
    Measure Theory Aspects of Locally Countable Orderings.Liang Yu - 2006 - 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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  26.  1
    Gray Matter Volume and Functional Connectivity in Hypochondriasis: A Magnetic Resonance Imaging and Support Vector Machine Analysis.Zhe Shen, Liang Yu, Zhiyong Zhao, Kangyu Jin, Fen Pan, Shaohua Hu, Shangda Li, Yi Xu, Dongrong Xu & Manli Huang - 2020 - Frontiers in Human Neuroscience 14.
    Objective: Patients with hypochondriasis hold unexplainable beliefs and a fear of having a lethal disease, with poor compliances and treatment response to psychotropic drugs. Although several studies have demonstrated that patients with hypochondriasis demonstrate abnormalities in brain structure and function, gray matter volume and functional connectivity in hypochondriasis still remain unclear.Methods: The present study collected T1-weighted and resting-state functional magnetic resonance images from 21 hypochondriasis patients and 22 well-matched healthy controls. We first analyzed the difference in the GMV between the (...)
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