bio | website | ims.nju.edu.cn/~yuliang |
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location | China | |
age | ||
visits | member for | 4 years |
seen | 3 hours ago | |
stats | profile views | 838 |
A mathematical logician.
Apr 17 |
awarded | Fanatic |
Apr 13 |
awarded | Yearling |
Apr 5 |
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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 |
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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 |
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Are there sets which are computable in one model, but uncomputable in another?
It would make induction fail. |
Nov 6 |
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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 |
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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
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
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Sep 29 |
answered | Sets computable from enough hints |
Sep 24 |
awarded | Autobiographer |
Jul 24 |
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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 |
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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 |
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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? |