Definability and Infinite Combinatorics:

The curious cases of MAD families and maximal cofinitary groups

David Schrittesser

A curious phenomenon in set theory is that often, objects which are constructed using the Axiom of Choice must display very irregular properties, and as such, cannot have a simple definition. An example for this are MAD families. It was somewhat of a surprise that very similarly defined objects, the maximally eventually different families, can be constructed even without using the Axiom of Choice, and in fact, they can be defined by a formula using very few quantifiers, making them very simple objects from the point of view of descriptive set theory.

In this course, which is intended for students which have already taken a course in set theory, we give detailed proofs of these results and discuss all the necessary prerequisites. The goal is to give a quick but thorough introduction which brings the student to the edge of current research, including some of the still open questions in this particular area.

Aspects of Determinacy

Alessandro Andretta

This course is aimed at students with some knowledge of basic logic and set theory. In the first part of the course we introduce the Axiom of Determinacy and show its consequences on the reals. In the second part we will look at more advanced results. Possible topics are: consequences of determinacy for the Turing degrees, measurability of \omega_1, the Wadge hierarchy.

lecture1:

8:30 am - 10:00 am(GMT+8)

lecture2:

10:30 am - 12:00 pm(GMT+8)

seminar:

14:00 pm - 16:00 pm(GMT+8)