论文标题
在Wadge等级$ω_2$周围的某些主题上
On some topics around the Wadge rank $ω_2$
论文作者
论文摘要
Kechris和Martin表明，在确定性的公理下，划分集合差差层次的$ω$ Theve的wadge等级为$ω_2$。在本文中，我们通过理解$ω$ -Th的$ω$ TH级别的差异差异层次结构，作为（相对）高氧化过程和有限的思想变更，差异差异。基于此ViewPiont，我们还通过将它们与$π^1_1 $ - 和$σ^1_1 $ - l-Least Number原理联系起来，研究了共同分析集的增加和减少差异层次结构之间的差距。我们还分析了相关原则的Weihrauch学位。
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.
