关于Wadge秩$ω_2$的几个问题
On some topics around the Wadge rank $ω_2$
摘要：
Kechris和Martin证明了在决定性公理下协分析集的递减差层次的$ω$ -级的Wadge秩是$ω_2$.在这篇文章中，我们给出了一个替代的证明Kechris-Martin定理，通过理解的$ω$ -第一级的递减差层次的协分析集作为（相对）超算术过程有限的心态变化。基于这一观点，我们还通过将协分析集的递增差层和递减差层分别与$Π^1_1$ -和$Σ^1_1$ -最小数原理联系起来，考察了它们之间的差距.并对相关原理的Weihrauch度进行了分析。
英文摘要：
Kechris and Martin showed that the Wadge rank of the $ω$-th level of the decreasing difference hierarchy of coanalytic sets is $ω_2$ under the axiom of determinacy. In this article, we give an alternative proof of the Kechris-Martin theorem, by understanding the $ω$-th level of the decreasing difference hierarchy of coanalytic sets as the (relative) hyperarithmetical processes with finite mind-changes. Based on this viewpiont, we also examine the gap between the increasing and decreasing difference hierarchies of coanalytic sets by relating them to the $Π^1_1$- and $Σ^1_1$-least number principles, respectively. We also analyze Weihrauch degrees of related principles.
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