**September 3**

**Joan Bagaria**,
Universitat de Barcelona

**Huge Reflection, and beyond**

We shall present some recent results from a joint work with Philipp Lücke on Structural Reflection at the upper ridges of the large-cardinal hierarchy. In particular, we will introduce a natural form of reflection we call 'Exact Reflection', giving upper and lower bounds for its consistency strength. We will also discuss 'sequential' forms of Exact Reflection, which may be viewed as strong forms of Chang's Conjecture, and which, in the case of infinite sequences, their strength goes beyond the strongest large cardinal principles that are not known to be inconsistent with the Axiom of Choice.