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Published or to be published:
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[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 $2\sp {\aleph\sb 0}$ 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 $\seq{\omega,\leq}$. To appear in the proceedings of the 13th International Congress of Logic Methodology and Philosophy of Science.
[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. to appear in APAL.
[pdf]
[22]Frank Stephan, Yue Yang and Liang Yu. Turing Degrees and The Ershov Hierarchy, to appear in the Proceedings of ALC 10.
[pdf]
[23]Joseph Miller and Liang Yu. Oscillation in the initial segment complexity of random reals. To appear in Advances in Mathematics.
[pdf]
[24]CT Chong, Wei Wang and Liang Yu. The strength of Projective Martin conjecture, Fundamenta Mathematicae, 207 (2010), 21-27.
[pdf]
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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]Johanna N.~Y.\ Franklin, Frank Stephan, and Liang Yu. Relativizations of Randomness and Genericity Notions. Preprint.
[pdf]
A set $A$ is a basis for Schnorr randomness if and only if it is
Turing reducible
to a set $R$ which is Schnorr random relative to $A$.
One can define a basis for weak $1$-genericity similarly.
It is shown that $A$ is a basis for Schnorr randomness if and only if
$A$ is a basis for weak $1$-genericity if and only if the halting
problem $K$ is not Turing reducible to $A$.
Furthermore, call a set $A$ high for Schnorr randomness versus Martin-L\"of
randomness if and only if every set which is Schnorr random relative
to $A$ is also
Martin-L\"of random unrelativized. It is shown that $A$ is high
for Schnorr randomness versus Martin-L\"of randomness if and only if
$K$ is Turing
reducible to $A$. Other results concerning highness for other pairs of
randomness notions are also included.
[4]Yun Fan and Liang Yu. The $cl$-maximal pairs of c.e. reals. Preprint.
[pdf]
For any non-computable $\Delta_2^0$ real, there exists a c.e. real
so that no c.e. real can $cl$-compute both of them. Thus, each
non-computable c.e. real is the half of a $cl$-maximal pair of
c.e. reals.
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