  We establish the descriptive set theoretic representation of the mouse
$M_n^{\#}$, which is called $0^{(n+1)\#}$. This part partially deals with the
case $n=2$ by proving the many-one equivalence of $M_2^{\#}$ and the theory of
$L_{\boldsymbol{\delta}^1_3}[T_3]$ with the higher level analogs of
$L$-indiscernibles.
