On July 9th, 2018 I gave a 90min talk in the Oberseminar Mathematical Logic at the University of Konstanz, Germany.

*Large cardinals from the determinacy of games*

*Abstract:* We will study infinite two player games and the large
cardinal strength corresponding to their determinacy. In particular,
we will consider mice, which are sufficiently iterable models of set
theory, and outline how they play an important role in measuring the
exact strength of determinacy hypotheses. After summarizing the
situation within the projective hierarchy for games of length
$\omega$, we will go beyond that and consider the determinacy of even
longer games. In particular, we will sketch the argument that
determinacy of analytic games of length $\omega \cdot (\omega+1)$
implies the consistency of $\omega+1$ Woodin cardinals. This part is
joint work with Juan P. Aguilera.