# Liang Yu

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 Name Liang Yu Member for 2 years Seen yesterday Website Location China Age
A mathematical logician.
 Apr13 awarded ● Yearling Apr3 comment Complexity of winning strategies for open games (for open player)Joel, you are right. There should be +1 there. Feb12 comment Complexity of winning strategies for open games (for open player)The rough idea is if the open player has a winning strategy, then for any node $\sigma$ with an even length in the tree $T$, we may define a partial function $f(\sigma)=\inf_n\sup_m f(\sigma ^{\smallfrown} n ^{\smallfrown}m)$ and ensure $f(\emptyset)$ always exists. Feb12 comment Complexity of winning strategies for open games (for open player)This was proved by Andreas Blass in A. Blass, Complexity of winning strategies, Discrete Math. 3 (1972), 295–300. " Feb9 comment Why has Sacks' “Measure-theoretic uniformity” not been more influential?He does not. But he used this fact. See the first sentence in section 4 at page 397. Feb9 comment Why has Sacks' “Measure-theoretic uniformity” not been more influential?Actually the results are quite natural from recursion theory point view. Essentially the whole results were just telling some "lowness phenomenon". If we replace $ZF$ with $KP$, then all the results remain true and become totally recursion theoretic. Feb9 comment Why has Sacks' “Measure-theoretic uniformity” not been more influential?The existence of an inaccessible cardinal is used to guarantee that there is a countable ordinal $\alpha$ so that $L_{\alpha}\models ZF+V=L$. Based on this, Sacks can perform a ramified analysis for random forcing to prove the results. Feb5 comment Countable admissible ordinalsTed, you are right. But the proof heavily depends on Jensen's theorem. Actually in the proof of Lemma 4.3, they need Lemma 3.3 that is Jensen's result. Feb4 comment Countable admissible ordinalsI asked Prof. Jensen, when he was in NUS, whether he has a model theoretical proof, or by applying Barwise compactness, of his result. He said no. So I guess Harrington's proof must be highly nontrivial. Feb4 comment Countable admissible ordinalsTed, thanks. In Simpon-Weitkamp's paper, it is claimed that Harrington has a model theoretical proof. But where to find it? Jan14 revised Definition of HYP in $L_{\omega_1^{CK}}[a]$?added 104 characters in body Jan14 revised Definition of HYP in $L_{\omega_1^{CK}}[a]$?added 512 characters in body Jan13 comment Definition of HYP in $L_{\omega_1^{CK}}[a]$?I fixed an error in the proof. To show that $x$ is not hyperarithemtic in $N$, we really need Leo's proof. Jan13 revised Definition of HYP in $L_{\omega_1^{CK}}[a]$?I fixed an error in the proof. Jan13 revised Definition of HYP in $L_{\omega_1^{CK}}[a]$?added 4 characters in body Jan13 revised Definition of HYP in $L_{\omega_1^{CK}}[a]$?added 29 characters in body Jan13 comment Road to Solovay’s Land.Having some recursion theory knowledge would also be very helpful to understand Solovay's construction. Jan12 comment Definition of HYP in $L_{\omega_1^{CK}}[a]$?$\Pi^0_1$-singletoness is not a absoluteness notion among the $\omega$-models. Also you have to apply Gandy's basis to get a model not the singleton. I added more details. Jan12 revised Definition of HYP in $L_{\omega_1^{CK}}[a]$?added 262 characters in body; added 11 characters in body Jan12 revised Definition of HYP in $L_{\omega_1^{CK}}[a]$?added 67 characters in body; added 14 characters in body Jan12 comment $\omega$-models of $\mathbf{\Sigma^1_1}-DC$ and $\mathbf{\Delta^1_1}-CA$ Check mathoverflow.net/questions/118706/… . It might be helpful for you. Jan12 answered Definition of HYP in $L_{\omega_1^{CK}}[a]$? Dec15 awarded ● Scholar Dec15 comment $\Delta^1_2$-well ordering vs $\Delta^1_3$Andres, thanks! I just got the paper. It seems that Leo also proved the lightface $\Delta^1_3$ one in the same paper. Dec15 asked $\Delta^1_2$-well ordering vs $\Delta^1_3$