Keita Yokoyama (JAIST)

Weihrauch degrees above arithmetical transfinite recursion

The studies of Weihrauch degrees and reverse mathematics share many ideas, and many similar results and close relations are known. The studies of Weihrauch degrees of the arithmetical transfinite recursion (ATR) and their relation to reverse mathematics are developed, e.g., in [1,2,3]. Typically, principles which are provable from $ATR_0$ (in the setting of reverse mathematics) by way of the pseudo-hierarchy method have various strengths. In this talk, we overview these situations and study the structure between ATR and the choice principle on the Baire space. This is joint work with Yudai Suzuki.

1. T. Kihara, A. Marcone and A. Pauly. Searching for an analogue of $ATR_0$ in the Weihrauch lattice. J. Symb. Log., 85(3):1006–1043, 2020.
2. Jun Le Goh. Some computability-theoretic reductions between principles around ATR0. arXiv preprint arXiv:1905.06868, 2019.
3. Paul-Elliot Anglès d'Auriac. Infinite Computations in Algorithmic Randomness and Reverse Mathematics. PhD thesis, Université Paris-Est, 2019.
4. Y. Suzuki and K. Yokoyama. Searching problems above arithmetical transfinite recursion. In preparation.