Mice with infinitely many Woodin cardinals from the determinacy of long games

(with J. Aguilera)

Neeman has shown that for any countable ordinal $\alpha$ the existence of a canonical inner model with $\alpha$ Woodin cardinals implies the determinacy of analytic games of transfinite length $\omega \cdot \alpha$. We show the converse of this result for $\alpha \in \omega$.

A preprint of this paper will be uploaded here soon.