[FOM] The necessity of forcing

joeshipman@aol.com 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 
provocative form:

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?

-- JS
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