[FOM] The necessity of forcing

[joeshipman@aol.com]

Jeremy, that doesn't work, because ZFC being consistent doesn't suffice 
to prove that "ZFC is not consistent" is not a theorem -- ZFC could be 
omega-inconsistent.

However, Bob Solovay pointed out that ZFC's "Rosser sentence"

"If there is a proof of me in ZFC, then there is an earlier proof of my 
negation"

does give a counterexample to my claim, so I have to modify it to 
instead say

Revised CLAIM:
There is no 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, where A is of mathematical importance.

-- JS

-----Original Message-----
From: jeremy.clark at wanadoo.fr
To: fom at cs.nyu.edu
Sent: Fri, 11 May 2007 1:41 AM
Subject: Re: [FOM] The necessity of forcing

What about A = "ZFC is consistent" ?

Jeremy Clark

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