[FOM] The necessity of forcing
joeshipman at aol.com
Thu May 10 12:29:36 EDT 2007
From private responses to my previous post, I satisfied myself that
forcing is useful for proving results about weaker systems than ZF, but
does not appear to be necessary for these. On the other hand, no one
responded to my last 2 queries, so I will restate them in a more
CLAIM: There is no important result (provable in ZFC) of the form
If ZFC is consistent, then neither A nor ~A is a theorem of ZFC
which has been proven without using forcing in at least one of the two
halves of the result.
Is anyone confident enough to either agree or disagree with this claim?
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