  We prove an iteration theorem which guarantees for a wide class of nice
iterations of $\omega_1$-preserving forcings that $\omega_1$ is not collapse,
at the price of needing large cardinals to burn as fuel. More precisely, we
show that a nice iteration of $\omega_1$-preserving forcings which force SRP at
successor steps and preserves old stationary sets does not collapse $\omega_1$.
