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

2020.11.20 Kenichi Abiko and Shohei Tanaka

Determinacy of Wadge games in Second Order Arithmetic / Game tree, ideas related to decent and generalized cost

• Date/Time: November 20, 2020 (Friday) / 15:00 - 17:00.

• Venue: Room 802, Science Complex A, Tohoku University.

• Speaker: Kenichi Abiko (東北大学大学院 理学研究科)

• Title: Determinacy of Wadge games in Second Order Arithmetic

• Abstract: Lipschitz and Wadge games were introduced by William W. Wadge as a tool for studying the complexity of subsets of real numbers. A. Louveau and J. Saint Raymond proved Second order arithmetic $$\mathrm{Z}_2$$ can prove that all Borel Wadge and Lipschitz games are determined. In this talk, we will introduce definition of Lipschitz and Wadge game and evaluate strength of subsystem of second order arithmetic which suffice to prove the determinacy of Lipschitz and Wadge games for first levels of Borel hierarchy. And we will see some reversal and open problems.

• Speaker: Shohei Tanaka

• Title: Game tree, ideas related to decent and generalized cost

• Abstract: Prof. Tanaka proved that decent & eigen-distribution implies PID of the tree. However, the concept of decent is somewhat awkward and complicated in the field of game tree therefore difficult to determine as we need derivatives to compute. In this talk, we will explain about how we could consider the weaker condition of decent, or some conditions we could think of. Also, we would mention the generalized cost, introduced by Peng and see how much work has done, and some works to be done.