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Published or to be published:

[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.[pdf]

[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. [pdf]

[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.[ps]

[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.
[pdf]

[6]Liang Yu. *Lowness for genericity.* Archive for Mathematical Logic 45 (2): 233-238 2006.
[ps]

[7]Liang Yu. *Measure theory aspects of Locally Countable Orderings.* Journal of Symbolic logic 71(3), 2006, pp. 958-968.
[pdf]

[8]Joseph Miller and Liang Yu. *On initial segment complexity and degrees of randomness.* Trans. Amer. Math. Soc. 360 (2008), 3193-3210.
[pdf]

[9]Rod Downey and Liang Yu. *Arithmetical Sacks Forcing.* Archive for Mathematical Logic 45(6) 715 - 720 2006.
[pdf]

[10]Liang Yu. *When van Lambalgen Theorem fails.* Proc. Amer. Math. Soc. 135 (2007), 861-864. [pdf]

[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.
[pdf]

[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.
[pdf]

[13]Yue Yang and Liang Yu. *Elementary differences among finite levels of the Ershov hierarchy.*
LNCS 3959: TAMC 2006, 765-771.
[pdf]

[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.[pdf]

[15]Chi-tat Chong and Liang Yu. *Maximal chains in the Turing degrees.* The Journal of Symbolic Logic, 72(2007), No 4, 1219-1227.
[pdf]

[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.
[pdf]

[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.
[pdf]

[18]Chitat Chong and Liang Yu. *A \Pi^1_1-Uniformization Principle for reals.* Trans. Amer. Math. Soc. 361 (2009), 4233-4245.
[pdf]

[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.
[pdf]

[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.
[pdf]

[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.
[pdf]

[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.
[pdf]

[23]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.
[pdf]

[24]CT Chong, Wei Wang and Liang Yu. *The strength of Projective Martin conjecture, * Fundamenta Mathematicae, 207 (2010), 21-27.
[pdf]

[25]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
[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 .
[pdf]

[27]Liang Yu. * A new proof of Friedman's conjecture.* The Bulletin of Symbolic Logic, 17, 3, pp. 455-461.
[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.
[pdf]

[29]Liang Yu. * Descriptive set theoretical complexity of randomness notions. * Fundamenta Mathematicae, 215, No. 3, 219-231 (2011).
[pdf]

[30]Wei Wang, Liuzhen Wu and Liang Yu. *Cofinal Maximal Chains in the Turing Degrees. * Proc. Amer. Math. Soc. 142 (2014), 1391-1398.
[pdf]

[31]Kengmeng Ng, Frank Stephan, Yue Yang and Liang Yu. * Computational aspects of the hyperimmune-free degrees. * A conferenc version is to appear in the 12th Proceedings of Asian Logic Conference.
[pdf]

[32]Frank Stephan and Liang Yu. * A reducibility related to being hyperimmune-free.* Annals of Pure and Applied Logic 165 (2014) 1291-1300.
[pdf]

Unpublished or under refereeing:

[1]Liang Yu. Some notes on ranked structures. unpublished.
[pdf]

We give a uniform proof of some results in \cite{GMta}. Moreover, we improve their results by
replacing hyperarithmetic with \Sigma^1_1.

[2]Decheng Ding, Wei Wang and Liang Yu. \Sigma_1 indiscernibles in c.e. degrees. unpublished.
[ps]

We study indiscernibles in the upper semi-lattice of computably enumerable Turing degrees.

[3]Liang Yu. Degree spectral of equivalence relations. Preprint.
[pdf]

In \cite{GMS11} and \cite{GMSnd}, Greenberg, Montalb{\'a}n and Slaman investigated both hyperarithmetic and constructibility degree spectral of countable structures. Inspired by their results, we push them to a more general setting by investigating degree spectrum of equivalence relations.

[4]CT Chong and Liang Yu. Randomness in the higher setting. Preprint.
[pdf]

We study the strengths of various notions of higher randomness: (i) strong \Pi^1_1-ML-randomness is separated from \Pi^1_1-ML-randomness; (ii) the hyperdegrees of \Pi^1_1-random reals are closed downwards (except for the trivial degree); (iii) the reals z in NCR_{\Pi^1_1} are precisely those satisfying z\in L_{\omega^z_1}, and (iv) lowness for \Delta^1_1-randomness is strictly weaker than that for \Pi^1_1-randomness.

[5] Rupert Holzl, Frank Stephan and Liang Yu. On Martin's Pointed Tree Theorem. Preprint.
[pdf]

We investigate the reverse mathematics strength of Martin's pointed tree theorem (\mathrm{MPT}) and its variation, weak Martin's pointed tree theorem (\mathrm{wMPT}).

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