bio | website | ims.nju.edu.cn/~yuliang |
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location | China | |
age | ||
visits | member for | 3 years, 8 months |
seen | 12 mins ago | |
stats | profile views | 804 |
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. |