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bio website ims.nju.edu.cn/~yuliang
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A mathematical logician.


May
17
comment Minimal degrees of structures
You don't need pb-genericity. It is not difficult to see that every ANC degree bounds a 1-generic degree (I think that it was already proved in the same DJS paper.)
Apr
23
comment Reference for “if the set $A$ is Suslin, then every $\Sigma^1_1(A)$ set is Suslin”
Have you checked Moschovakis book? or Cabal seminar?
Apr
17
awarded  Fanatic
Apr
13
awarded  Yearling
Apr
5
comment Degree of unsolvability of finding a open approximation to a Borel set, given its Borel code
Peter Hinman (Hinman, Peter G. Some applications of forcing to hierarchy problems in arithmetic. Z. Math. Logik Grundlagen Math. 15 1969 341–352. ) investigated something related your question based on Sacks work.
Apr
4
answered Degree of unsolvability of finding a open approximation to a Borel set, given its Borel code
Mar
10
answered Borel cross section
Jan
26
comment Adding a real with infinite conditions
Jockusch told me that a similar method (restrict the conditions with the recursive ones) was also used by Spector, and later by Lachlan, to construct minimal Turing degrees.
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
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Sep
29
revised Sets computable from enough hints
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Sep
29
revised Sets computable from enough hints
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Sep
29
revised Sets computable from enough hints
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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.