bio  website  ims.nju.edu.cn/~yuliang 

location  China  
age  
visits  member for  3 years, 3 months 
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A mathematical logician.
19h

comment 
The (global) theory of Borel equivalence relations
At least the LouveauVelickovic's result implies the $\Sigma_1$theory of $(\mathcal{B},\leq_B)$ is decidable. 
1d

answered  Are lightface \Delta11 classes of reals describable with hyperarthmetic formulae? 
1d

comment 
Are lightface \Delta11 classes of reals describable with hyperarthmetic formulae?
This is a reformulation of the well known result due to Kleene which says that every $\Delta^1_1$ set of reals has a recursive Borel code. The details can be found either in Moschovakis book or Thm 2.7.2 in my joint book with CT. 
Jul 20 
answered  Borel Sets in Sacks Generic Extension 
Jul 8 
comment 
Decomposing $\mathbf{\Pi}^1_1$ sets into closed sets
Dilip had a similar idea to Paul's. I think the direct method should work. A further question is whether every Borel set can be decomposed into $\aleph_1$ many disjoint closed sets? 
Jul 8 
accepted  Decomposing $\mathbf{\Pi}^1_1$ sets into closed sets 
Jul 2 
awarded  Curious 
Jul 1 
comment 
MartinLöf randomness relative to a $\Delta^0_2$representation of a real
If $x$ is random and $\geq_T \emptyset'$, then any low for $x$ real is $GL_1$. 
Jun 18 
awarded  Revival 
Jun 18 
answered  MartinLöf randomness relative to a $\Delta^0_2$representation of a real 
Jun 10 
comment 
Higher recursion theory and reverse mathematics: What is to $\Pi^1_1CA_0$ as $RCA_0$ is to $ACA_0$?
@Denis, good idea. But when you talk about induction, you need a well ordering. My vague ideal is that infinitary logic might be a right way to make this sense. 
Jun 5 
revised 
A “suitably generic” set of Cohen reals without forcing?
added 13 characters in body 
Jun 4 
revised 
A “suitably generic” set of Cohen reals without forcing?
added 157 characters in body 
Jun 4 
answered  A “suitably generic” set of Cohen reals without forcing? 
May 28 
accepted  Demuth's theorem in set theory 
May 27 
revised 
Demuth's theorem in set theory
edited body 
May 27 
revised 
Demuth's theorem in set theory
added 1042 characters in body 
May 26 
comment 
Martin's cone theorem and recursion theory
I would like to add a remark that it can be shown that the base is not second order arithmetic definable. 
May 26 
revised 
Demuth's theorem in set theory
edited title 
May 26 
comment 
Demuth's theorem in set theory
I was just kidding. Thanks for pointing out this. 