Title of the course: Axiom of determinacy and some of its consequences
Instructor: Asst. Prof. Burak Kaya
Institution: ODTÜ
Dates: 10-16 Eylül 2018
Prerequisites: Exposure to topology of metric spaces is required. Little exposure to Lebesgue measure is suggested but not required, as we shall go over the construction. It may help to be acquainted with the axiom of choice and its variants, though, knowledge on axiomatic set theory is not required.
Level: Graduate, advanced undergraduate
Abstract: We shall first introduce infinite games on natural numbers and the axiom of determinacy (AD) which states that all such games have winning strategies for one of the two players. We will then cover some consequences of AD, without assuming the axiom of choice. Finally, we will cover some determinacy results such as the Gale-Stewart theorem, assuming the axiom of choice.
Textbook or/and course webpage: Relevant parts of the book “Set Theory, The Third Millenium Edition” by Thomas Jech. The instructor will also provide some lecture notes.
Language: TR, EN