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Publications before 2011 (The papers are available upon request.)
Publications before 2011 (The papers are available upon request.)
[1]Yue Yang and Liang Yu. On the Definable Ideal Generated by Nonbounding C.E.~Degrees. Journal of Symbolic logic, 70(2005), No.1, 252-270.
[2]Decheng Ding, Rod Downey, and Liang Yu. The Kolmogorov complexity of random reals. Ann. Pure Appl. Logic 129 (2004), no. 1-3, 163--180.
[3]Decheng Ding and Liang Yu. There are 2^{\aleph_0} many H-degrees in the random reals. Proc. Amer. Math. Soc. 132 (2004), no. 8, 2461--2464.
[4]Decheng Ding and Liang Yu. There is no SW-complete c.e. real. J. Symbolic Logic 69 (2004), no. 4, 1163-1170.
[5]Rod Downey and Liang Yu. There are no maximal low d.c.e. degrees. Notre Dame J. Formal Logic 45 (2004), no. 3, 147- 159.
[6]Liang Yu. Lowness for genericity. Archive for Mathematical Logic 45 (2): 233-238 2006.
[7]Liang Yu. Measure theory aspects of Locally Countable Orderings. Journal of Symbolic logic 71(3), 2006, pp. 958-968.
[8]Joseph Miller and Liang Yu. On initial segment complexity and degrees of randomness. Trans. Amer. Math. Soc. 360 (2008), 3193-3210.
[9]Rod Downey and Liang Yu. Arithmetical Sacks Forcing. Archive for Mathematical Logic 45(6) 715 - 720 2006.
[10]Liang Yu. When van Lambalgen Theorem fails. Proc. Amer. Math. Soc. 135 (2007), 861-864.
[11]Rod Downey, Andrea Nies, Rebecca Weber, Liang Yu. Lowness and \Pi_2^0 Nullsets. Journal of Symbolic logic 71(3), 2006, pp. 1044-1052.
[12]Yue Yang and Liang Yu. \mathcal{R} is not a \Sigma_1-elementary substructure of \mathcal{D}_n. Journal of Symbolic logic, 71(2006), No.4, 1223-1236.
[13]Yue Yang and Liang Yu. Elementary differences among finite levels of the Ershov hierarchy. LNCS 3959: TAMC 2006, 765-771.
[14]Frank Stephan and Liang Yu. Lowness for weakly 1-generic and Kurtz-random. A conference version was appeared in LNCS 3959: TAMC 2006,756-764.
[15]Chi-tat Chong and Liang Yu. Maximal chains in the Turing degrees. The Journal of Symbolic Logic, 72(2007), No 4, 1219-1227.
[16]Chi-tat Chong, Andre Nies and Liang Yu. Higher randomness notions and their lowness properties. Israel Journal of Mathematics, 166(2008), No 1, 39-60.
[17]Chi-tat Chong and Liang Yu. Thin Maximal Antichains in the Turing Degrees. A conference versoin was appeared in Vol 4497 of LNCS, 162-168, CiE2007.
[18]Chitat Chong and Liang Yu. A \Pi^1_1-Uniformization Principle for reals. Trans. Amer. Math. Soc. 361 (2009), 4233-4245.
[19] Rod Downey, Bakhadyr Khoussainov, Joseph Miller and Liang Yu. Degree Spectra of Unary Relations on L(\omega,\leq). Logic, Methodology and Philosophy of Science: Proceedings of the Thirteenth International Congress, pages 35--55. College Publications, 2009.
[20]Klaus Ambos-Spies, Decheng Ding, Wei Wang and Liang Yu. Bounding Non-GL_2 and R.E.A.. The Journal of Symbolic Logic, 74(2009), No 3, 989-1000.
[21]Bjorn Kjos-Hanssen, Andre Nies, Frank Stephan and Liang Yu. Higher Kurtz randomness. Annals of Pure and Applied Logic, Volume 161, Issue 10, July 2010, Pages 1280-1290.
[22]Frank Stephan, Yue Yang and Liang Yu. Turing Degrees and The Ershov Hierarchy,Proceedings of the Tenth Asian Logic Conference, Kobe, Japan, 1-6 September 2008, World Scientific, pages 300-321, 2009.
[23]CT Chong, Wei Wang and Liang Yu. The strength of Projective Martin conjecture, Fundamenta Mathematicae, 207 (2010), 21-27.
Publications after 2010
Publications after 2010
[24]Yun Fan and Liang Yu. The cl-maximal pairs of c.e. reals. Annals of Pure and Applied Logic, 162(5), Feb-March 2011, Pages 357-366.
clm.pdf[25]Joseph Miller and Liang Yu. Oscillation in the initial segment complexity of random reals. Advances in Mathematics. Volume 226, Issue 6, 1 April 2011, Pages 4816-4840.
oscillation.pdf[26]Johanna N.~Y.\ Franklin, Frank Stephan, and Liang Yu. Relativizations of Randomness and Genericity Notions. Bull. London Math. Soc. (2011) 43(4): 721-733 .
fsy.pdf[27]Liang Yu. A new proof of Friedman's conjecture. The Bulletin of Symbolic Logic, 17, 3, pp. 455-461.
friedman.pdf[28]Liang Yu. Characterizing strong randomness via Martin-L\" of randomness. Annals of Pure and Applied Logic, Volume 163, Issue 3, March 2012, Pages 214-224.
x.pdf[29]Liang Yu. Descriptive set theoretical complexity of randomness notions. Fundamenta Mathematicae, 215, No. 3, 219-231 (2011).
madison.pdf[30]Wei Wang, Liuzhen Wu and Liang Yu. Cofinal Maximal Chains in the Turing Degrees. Proc. Amer. Math. Soc. 142 (2014), 1391-1398.
pams14.pdf[31]Kengmeng Ng, Frank Stephan, Yue Yang and Liang Yu. Computational aspects of the hyperimmune-free degrees. Conference version: Proceedings of the 12th Asian Logic Conference: pp. 271-284.
hif_ALC.pdf[32]Frank Stephan and Liang Yu. A reducibility related to being hyperimmune-free. Annals of Pure and Applied Logic 165 (2014),1291-1300.
shifdegree.pdf[33]Liang Yu. Degree spectral of equivalence relations. Proceedings of the 13th Asian Logic Conference, 237-242, 2015.
spe.pdf[34]CT Chong and Liang Yu. Randomness in the higher setting. The Journal of Symbolic Logic, 80 (2015), pp 1131-1148.
cy8.pdf[35]Rupert Holzl, Frank Stephan and Liang Yu. On Martin's Pointed Tree Theorem. Computability, vol. 5, no. 2, pp. 147-157, 2016.
HSY.pdf[36]CT Chong and Liang Yu. Measure-theoretic applications of higher Demuth's theorem. Trans. Amer. Math. Soc. 368 (2016), pp. 8249-8265.
hd6.pdf[37]Liang Yu and Yizheng Zhu. On the reals which cannot be random. Computability and Complexity: Essays Dedicated to Rodney G. Downey on the Occasion of His 60th Birthday, Lecture Notes in Computer Science, 611--622, Vol.10010, 2017. (Some minor errors in the published version were corrected.)
ncr4.pdf[38]Mariam Beriashvili, Ralf Schindler, Liuzhen Wu, Liang Yu, Hamel bases and well-ordering the continuum, Proceedings of AMS, Volume 146, Number 8, August 2018, Pages 3565–3573.
hamel.pdf[39]Wolfgang Merkle, Liang Yu, Being low along a sequence and elsewhere, The Journal of Symbolic Logic, Volume 84, Issue 2 June 2019 , pp. 497-516.
low-along-jslc.pdf[40]CT Chong, Liuzhen Wu and Liang Yu, BASIS THEOREMS FOR $\Sigma^1_2$-SETS, The Journal of Symbolic Logic, 11 February 2019, pp. 376-387
cwyfinal.pdf[41]Rupert Holz, Wolfgang Merkle, Joseph Miller, Frank Stephan, Liang Yu, Chaitin'S Ω as a continuous function. The Journal of Symbolic Logic, March 2020, 85(1), 486-510.
omega23.pdf[42] Liang Yu, An application of recursion theory to analysis. Bulletin of Symbolic Logic , Volume 26 , Issue 1 , March 2020 , pp. 15 - 25.
johnson4.pdf[43] Yinhe Peng and Liang Yu, TD implies CCR. Advances in Mathematics, Volume 384, June 2021.
tdccr2.pdf[44] Arno Pauly, Linda Westrick and Liang Yu, Luzin's (N) and randomness reflection. The Journal of Symbolic Logic, Volume 87, Issue 2, June 2022, 802-828.
luzinsn.pdf[45] Keng Meng Ng, Frank Stephan, Yue Yang and Liang Yu, On Trees without Hyperimmune Branches. Revolutions and Revelations in Computability: 18th Conference on Computability in Europe, CiE 2022, Swansea, UK, July 11–15, 2022, Proceedings.
ng-stephan-yang-yu.pdf[46] Yinhe Peng, Liuzhen Wu, and Liang Yu, Some consequences of $\TD$ and $\sTD$, The Journal of Symbolic Logic. 2023;88(4):1573-1589.
tdstd10.pdf[47] Jack Lutz, Renrui Qi, Liang Yu, The Point-to-Set Principle and the Dimensions of Hamel Bases, Computability 13 (2024),. 105-112. [arxiv]
[48] Benoit Monin and Liang Yu, On the Borelness of upper cones of hyperdegrees. Cummings, James and Marks, Andrew and Yang, Yue and Yu, Liang, Higher Recursion Theory and Set Theory, Volume 44 of the Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore, WORLD SCIENTIFIC.
borel2.pdf[49] Liang Yu, Some more results on relativized Chaitin's $\Omega$., Ann. Pure Appl. Logic 176 (2025), no. 8, Paper No. 103586.
rdorder2.pdf[50] Nan Fang, Lu Liu, Liang Yu,; Integer-valued martingales and cl-Turing reductions. Theoret. Comput. Sci. 1040 (2025), Paper No. 115202
ivrclm_v1.pdfBooks or proceedings I edited:
[1] Chong, Chi Tat; Yu, Liang Recursion theory. Computational aspects of definability. (English) De Gruyter Series in Logic and Its Applications 8. Berlin: De Gruyter (ISBN 978-3-11-027555-1 ). xiii, 306 p. (2015).
[2] Zhao, Xishun; Feng, Qi; Kim, Byunghan; Yu, Liang Proceedings of the 13th Asian logic conference, ALC 2013, Guangzhou, China, September 16–20, 2013. (English), NJ: World Scientific (ISBN 978-981-4675-99-4). x, 242 p. (2015).
[3] Kim, Byunghan; Brendle, Jörg; Lee, Gyesik; Liu, Fenrong ; Ramanujam, R. ; Srivastava, Shashi M. ; Tsuboi, Akito; Yu, Liang Proceedings of the 14th and 15th Asian logic conferences, Mumbai, India, January, 5–8, 2015 and Daejeon, South Korea, July 10–14, 2017. (English) NJ: World Scientific (ISBN 978-981-323-754-4). xii, 297 p. (2019).
[4] Peng, NingNing; Tanaka, Kazuyuki; Yang, Yue; Wu, Guohua; Yu, Liang Computability theory and foundations of mathematics. Proceedings of the 9th international conference on computability theory and foundations of mathematics, Wuhan, China, March 21–27, 2019. (English) Singapore: World Scientific (ISBN 978-981-12-5928-9/hbk; 978-981-125-930-2/ebook). 188 p. (2022).
Not published yet.
Not published yet.
[1] JORG BRENDLE, FABIANA CASTIBLANCO, RALF SCHINDLER, LIUZHEN WU, AND LIANG YU, A MODEL WITH EVERYTHING EXCEPT FOR A WELL-ORDERING OF THE REALS
We construct a model of ZF + DC containing a Luzin set, a Sierpinski set, as well as a Burstin basis but in which there is no a well ordering of the continuum.
specialsets.pdf[2] Sirun Song and Liang Yu, On the Hausdorff dimension of maximal chains and antichains of Turing and Hyperarithmetic degrees. [arxiv]
This paper investigates the Hausdorff dimension properties of chains and antichains in Turing degrees and hyperarithmetic degrees. Our main contributions are threefold: First, for antichains in hyperarithmetic degrees, we prove that every maximal antichain necessarily attains Hausdorff dimension 1. Second, regarding chains in Turing degrees, we establish the existence of a maximal chain with Hausdorff dimension 0. Furthermore, under the assumption that \omega_1=(\omega_1)^L, we demonstrate the existence of such maximal chains with \Pi^1_1 complexity. Third, we extend our investigation to maximal antichains of Turing degrees by analyzing both the packing dimension and effective Hausdorff dimension.
[3] Jinhe Ye, Liang Yu and Xuangheng Zhao, When is $A + x A =\mathbb{R}$. [arxiv]
We show that there is an additive $F_\sigma$ subgroup $A$ of $\mathbb{R}$ and $x \in \mathbb{R}$ such that $\mathrm{dim_H} (A) = \frac{1}{2}$ and $A + x A =\mathbb{R}$. However, if $A \subseteq \mathbb{R}$ is a subring of $\mathbb{R}$ and there is $x \in \mathbb{R}$ such that $A + x A =\mathbb{R}$, then $A=\mathbb{R}$. Moreover, assuming the continuum hypothesis (CH), there is a subgroup $A$ of $\mathbb{R}$ with $\mathrm{dim_H} (A) = 0$ such that $x \not\in \mathbb{Q}$ if and only if $A + x A =\mathbb{R}$ for all $x \in \mathbb{R}$. A key ingredient in the proof of this theorem consists of some techniques in recursion theory and algorithmic randomness. We believe it may lead to applications to other constructions of exotic sets of reals. Several other theorems on measurable, and especially Borel and analytic subgroups and subfields of the reals are presented. We also discuss some of these results in the $p$-adics.
Some notes.
Some notes.
[1] Harrington, The hyperdegrees of reals in products of uncountable $\Sigma^1_1$ sets, September, 1975.
Typed by Hongyuan Yu. I made some notes.
harrington-product.pdf[2] Jensen, Coding a finite sequence of countable admissible ordinals.
Typed by Xiuyuan Sun. The proof is recursion theoretic.
admissible.pdfGoogle Sites
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