I am invited to give a plenary talk at the congress of the Italian Association of Logic and Applications in Udine, taking place September 3-6, 2024.

*Infinite Games and Large Cardinals: Attacking Independence by Connecting the Hierarchies*

The independence phenomenon is a central theme in set theory. Moreover, starting from the Continuum Problem, there are numerous statements in various areas of mathematics that can neither be proven nor disproven in the usual axiomatic framework given by the Zermelo Fraenkel Axioms. The most promising approach to attack this issue is by studying extensions of the usual axiomatic framework, their connections, and their impact on previously independent statements. Two famous examples in set theory are the hierarchies given by the determinacy of infinite two-player games and large cardinals. The deep connection between these two hierarchies forms the backbone of inner model theory. We outline this connection and discuss recent progress as well as important open questions in the area.