**
Julian Bradfield
** - Fixpoints, Games and Arithmetic

For some decades, it has been known that inductive definitions (alias least fixpoints) are intimately related to certain games. In particular, there were nice relations via the so-called game quantifier between inductively definable sets and the first two levels of the arithmetical hierarchy. In the temporal logic community, it is also well known that fixpoint alternation corresponds to certain games. In this talk, I'll describe how the set-up in the temporal logic world transfers back nicely to the world of descriptive set theory, so extending the old results in a natural way.