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814
bio website ims.nju.edu.cn/~yuliang
location China
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visits member for 3 years, 3 months
seen 26 secs ago

A mathematical logician.


19h
comment The (global) theory of Borel equivalence relations
At least the Louveau-Velickovic's result implies the $\Sigma_1$-theory of $(\mathcal{B},\leq_B)$ is decidable.
1d
answered Are lightface \Delta-1-1 classes of reals describable with hyperarthmetic formulae?
1d
comment Are lightface \Delta-1-1 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 Martin-Löf 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 Martin-Löf randomness relative to a $\Delta^0_2$-representation of a real
Jun
10
comment Higher recursion theory and reverse mathematics: What is to $\Pi^1_1-CA_0$ 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.