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bio website ims.nju.edu.cn/~yuliang
location China
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visits member for 3 years, 8 months
seen 12 mins ago

A mathematical logician.


Nov
6
comment Are there sets which are computable in one model, but uncomputable in another?
It would make induction fail.
Nov
6
comment Are there sets which are computable in one model, but uncomputable in another?
Concerning the last question. Any infinite subset of $(\mathbb{N})^U$ in $U$ does not exist in any proper extension $V$ of $U$. Otherwise, $(\mathbb{N})^U$ belongs to $V$, a contradiction.
Sep
30
comment Sets computable from enough hints
@Dan, you are right. Thanks.
Sep
29
revised Sets computable from enough hints
edited body
Sep
29
revised Sets computable from enough hints
added 6 characters in body
Sep
29
revised Sets computable from enough hints
added 120 characters in body
Sep
29
revised Sets computable from enough hints
deleted 2 characters in body
Sep
29
answered Sets computable from enough hints
Sep
24
awarded  Autobiographer
Jul
24
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.
Jul
23
answered Are lightface \Delta-1-1 classes of reals describable with hyperarthmetic formulae?
Jul
23
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.