Liang Yu
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Registered User
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A mathematical logician.
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Apr 13 |
awarded | ● Yearling |
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Apr 3 |
comment |
Complexity of winning strategies for open games (for open player) Joel, you are right. There should be +1 there. |
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Feb 12 |
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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. |
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Feb 12 |
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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. " |
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Feb 9 |
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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. |
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Feb 9 |
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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. |
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Feb 9 |
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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. |
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Feb 5 |
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Countable admissible ordinals Ted, 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. |
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Feb 4 |
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Countable admissible ordinals I 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. |
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Feb 4 |
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Countable admissible ordinals Ted, thanks. In Simpon-Weitkamp's paper, it is claimed that Harrington has a model theoretical proof. But where to find it? |
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Jan 14 |
revised |
Definition of HYP in $L_{\omega_1^{CK}}[a]$? added 104 characters in body |
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Jan 14 |
revised |
Definition of HYP in $L_{\omega_1^{CK}}[a]$? added 512 characters in body |
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Jan 13 |
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. |
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Jan 13 |
revised |
Definition of HYP in $L_{\omega_1^{CK}}[a]$? I fixed an error in the proof. |
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Jan 13 |
revised |
Definition of HYP in $L_{\omega_1^{CK}}[a]$? added 4 characters in body |
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Jan 13 |
revised |
Definition of HYP in $L_{\omega_1^{CK}}[a]$? added 29 characters in body |
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Jan 13 |
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Road to Solovay’s Land. Having some recursion theory knowledge would also be very helpful to understand Solovay's construction. |
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Jan 12 |
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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. |
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Jan 12 |
revised |
Definition of HYP in $L_{\omega_1^{CK}}[a]$? added 262 characters in body; added 11 characters in body |
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Jan 12 |
revised |
Definition of HYP in $L_{\omega_1^{CK}}[a]$? added 67 characters in body; added 14 characters in body |
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Jan 12 |
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$\omega$-models of $\mathbf{\Sigma^1_1}-DC$ and $\mathbf{\Delta^1_1}-CA$ Check mathoverflow.net/questions/118706/… . It might be helpful for you. |
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Jan 12 |
answered | Definition of HYP in $L_{\omega_1^{CK}}[a]$? |
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Dec 15 |
awarded | ● Scholar |
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Dec 15 |
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$\Delta^1_2$-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. |
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Dec 15 |
asked | $\Delta^1_2$-well ordering vs $\Delta^1_3$ |
