[FOM] CH and forcing
Roger Bishop Jones
rbj at rbjones.com
Sun Jul 3 16:45:16 EDT 2011
I have twice recently read the following assertion:
"Every model of ZFC has a forcing extension in which CH
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?
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