Lightface mice with finitely many Woodin cardinals from optimal   determinacy hypotheses
  The determinacy of lightface $\Delta^1_{2n+2}$ and boldface $\boldsymbol{\Pi}^1_{2n+1}$ sets implies the existence of an $(\omega, \omega_1)$-iterable $M_{2n+1}^{\#}$. 
Yizheng Zhu
math.LO