[FOM] CH and forcing

[Robert Solovay]

Perhaps they are allowing Boolean valued extensions?

-- Bob Solovay

On Sun, Jul 3, 2011 at 1:45 PM, Roger Bishop Jones <rbj at rbjones.com> wrote:
> I have twice recently read the following assertion:
>
> "Every model of ZFC has a forcing extension in which CH
> fails."
>
> Once by Woodin, and once by Hamkins.
>
> "Every model" is clearly too strong here, since not every
> model has any extensions at all (and the truth value of CH
> in second order ZFC is not known).
>
> "Every countable transitive model" is more like the result
> usually proven, and the proof as I understand it does depend
> on the model being countable.
>
> Is there a stronger result?
>
> Roger Jones
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