Sendai Logic Mathematical Institute, Tohoku University, Sendai, Miyagi, Japan

#### 2020.10.09 Leonardo Pacheco

A Look Into the Structure of the Wadge Degrees

• Date/Time: October 9, 2020 (Friday) / 15:00 - 16:00.

• Speaker: Leonardo Pacheco (東北大学大学院 理学研究科)

• Venue: Rm 802, Science Complex A, Tohoku Univ.

• Abstract: The Wadge degrees were defined by William Wadge in his PhD thesis. Wadge also gave two classifications of the Wadge degrees below $$\bold{\Sigma}^0_3$$. The first of these was extended up to the Borel sets by Louveau, and the second was also extended up to the Borel sets by Duparc. Later, Fournier extended both of the classifications up to the collection of increasing differences of $$\bold{\Pi}^1_1$$ sets.
In this presentation we sketch these two classifications and the extentions given by Fournier.