[FOM] Eliminability of AC

joeshipman@aol.com joeshipman at aol.com
Sun Mar 30 22:59:26 EDT 2008

That's an excellent example, and now that you have jogged my memory I 
believe they did use Absoluteness to eliminate GCH.

Kochen's student Scott Brown in 1978 gave a computable bound for the 
relevant results involving a very high stack of iterated exponentials 
(at least 7 is my recollection).

-- JS
-----Original Message-----
From: Robert M. Solovay <solovay at math.berkeley.edu>
To: Foundations of Mathematics <fom at cs.nyu.edu>
Sent: Sun, 30 Mar 2008 5:28 am
Subject: Re: [FOM] Eliminability of AC

I believe the original proofs of Ax and Kochen of their results
concedrning p-adic fields used the theory of ultraproducts in a way 
required GCH. Since the results obtained were arithmetic, one could 
invoke the Kreisel remark to disentangle their results from GCH.

I don't recall at this late date whether Ax and Kochen made this
observation themselves.

     --Bob Solovay

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