# Re: Paper and slides on indefiniteness of CH

Dear Sy,

Thanks, that helps. But just to be clear, does $\textsf{SIMH}^\#$ imply the  following statement?

If $\varphi$ holds of $\omega_1^V$ in a #-generated outer model of V which preserves $\omega_1^V$ then $\varphi$ holds of $\omega_1^V$ in an inner model of V.

The reason I ask is that for $\textsf{SIMH}$, the analogous statement (deleting #-generated) holds and is implied by $\textsf{SIMH}(\omega_1)$.

Regards,
Hugh