Re: Paper and slides on indefiniteness of CH

Dear Sy,

So what is \textsf{SIMH}^\#(\omega_1)? You wrote in your message of Sept 29:

The \textsf{IMH}^\# is compatible with all large cardinals. So is the  \textsf{SIMH}^\#(\omega_1)

A second question. The version of  \textsf{SIMH}^\# you specified in your next message to me on Sept 29:

The (crude, uncut) \textsf{SIMH}^\# is the statement that V is #-generated and if a sentence with absolute parameters holds in a cardinal-preserving, #-generated outer model then it holds in an inner model. It implies a strong failure of CH but is not known to be consistent.

does not even obviously imply \textsf{IMH}^\#.  Perhaps you meant, the above together with \textsf{IMH}^\#? If not then calling it \textsf{SIMH}^\# is rather misleading. Either way it is closer to \textsf{IMH}^\#(\text{card}).

Anyway this explains my confusion, thanks.

Regards,
Hugh

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