A Survey of Determinacy of Infinite Games in Second Order Arithmetic

Dedicated to Professor Tanaka's 60th birthday

Abstract

In the conference of Computability Theory and Foundations of Mathematics 2015, we had special sessions on Professor Kazuyuki Tanaka's work in honor of his 60th birthday. It was a great honor for me to give a talk about determinacy of infinite games in that session. In this paper, accordance with works by Professor Tanaka on determinacy, we introduce a collection of related researches.