On some topics around the Wadge rank $\omega_2$

Takayuki Kihara

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arXiv · 2201.12472

On some topics around the Wadge rank $\omega_2$

Takayuki Kihara

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Abstract

Kechris and Martin showed that the Wadge rank of the $\omega$-th level of the decreasing difference hierarchy of coanalytic sets is $\omega_2$ under the axiom of determinacy. In this article, we give an alternative proof of the Kechris-Martin theorem, by understanding the $\omega$-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 $\Pi^1_1$- and $\Sigma^1_1$-least number principles, respectively. We also analyze Weihrauch degrees of related principles.

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BibTeX RIS

Takayuki Kihara. 2022-01-29. On some topics around the Wadge rank $\omega_2$. https://arxiv.org/abs/2201.12472

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