I have been asked to be part of the Scientific committee for the sixth Young set theory workshop, to be held in Piamonte, Italy, during a week in Spring 2013. The other members of the committee are Matteo Viale (chair), Asgard Tornquist, Sean Cox, and Andrew Brooke-Taylor.
- James Cummings – Large cardinals: PCF-theory and its interactions with large cardinals, forcing and -like combinatorial principles. The tutorial will focus on applications of Shelah’s PCF-theory outside cardinal arithmetic, including constructions for Jónsson algebras, strong covering lemmas, and constructions for almost-free, non-free objects.
- Sy David Friedman – Forcing and combinatorial set theory: Descriptive set theory on . Assuming GCH, most of the basic notions of classical descriptive set theory generalize easily from Baire space to generalized Baire space , for an uncountable regular cardinal . But many of the theorems do not. The tutorial will discuss regularity properties and the Borel reducibility of deﬁnable equivalence relations in the generalized setting.
- Su Gao – Descriptive Set Theory: Borel markers in the study of countable Borel equivalence relations. The tutorial will give an introduction to the theory of Borel markers in the study of countable Borel equivalence relations. Borel markers are important tools used to attach structures to the classes of countable Borel equivalence relations. They play a prominent role in the study of hyperﬁnite and treeable equivalence relations, and have applications in other topics such as the computation of Borel chromatic numbers.
- John Steel – Inner Model Theory: Iteration Trees. The tutorial will cover the basic theory of iteration trees, and some of its applications. It starts at a basic level, deﬁning ultrapowers of models of ZFC and their properties, and tries to keep the presentation accessible to anyone who has taken a graduate-level course in set theory. (In particular, no background in inner model theory will be assumed.)
I will add more details as they are decided, we expect to invite five post doctoral researchers to give one hour talks. For now, here are the links to the previous workshops: