Re: Paper and slides on indefiniteness of CH

Dear Hugh,

Sorry for my delayed response.

For the purposes of this discussion:

The \textsf{IMH}^\# is the statement that V is #-generated and if a sentence holds in a #-generated outer model then it holds in an inner model. It is consistent with all large cardinals.

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.

The reason that the \textsf{IMH}^\# can be shown to be consistent is that Jensen coding works for #-generated models.

The reason that the \textsf{SIMH}^\#  is not known to be consistent is that Jensen coding will collapse cardinals if GCH fails.

I hope that this clarifies the situation.

Thanks for your interest,
Sy

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