Mice with finitely many Woodin cardinals from optimal determinacy hypotheses

Sandra Müller, Ralf Schindler, W. Hugh Woodin

We prove the following result which is due to the third author. Let $n\ge 1$. If ${\mathbf{\Pi }}_n^1$ determinacy and ${\Pi }_{n+1}^1$ determinacy both hold true and there is no $\bolds…