Papers
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
[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] Benoit Monin and Liang Yu, On the Borelness of upper cones of hyperdegrees. To appear in the proceedings dedicated to Ted Slaman and Hugh Woodin.
borel2.pdf[44] Yinhe Peng and Liang Yu, TD implies CCR. Advances in Mathematics, Volume 384, June 2021.
tdccr2.pdf[45] 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[46] 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[47] Yinhe Peng, Liuzhen Wu, and Liang Yu, Some consequences of $\TD$ and $\sTD$, JSL, The Journal of Symbolic Logic. 2023;88(4):1573-1589.
tdstd10.pdf[48] Jack Lutz, Renrui Qi, Liang Yu, The Point-to-Set Principle and the Dimensions of Hamel Bases, Computability, to appear. [arxiv]
Books 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.
[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] Liang Yu, Some more results on relativized Chaitin's $\Omega$.
We prove that, assuming $\ZF$, and restricted to any pointed set, Chaitin's $\Omega_U:x\mapsto \Omega_U^x=\sum_{U^x(\sigma)\downarrow}2^{-|\sigma|}$ is not injective for any universal prefix-free Turing machine $U$, and that $\Omega_U^x$ fails to be degree invariant in a very strong sense, answering several recent questions in descriptive set theory. Moreover, we show that under $\ZF+\AD$, every function $f$ mapping $x$ to $x$-random must be uncountable-to-one over an upper cone of Turing degrees.
rdorder2.pdfSome 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.