[FOM] inconsistency of PA

Robert M. Solovay solovay at math.berkeley.edu
Thu May 6 00:22:37 EDT 2004

Randall's proof [which I have been thinking about for the last few hours]
is indeed erroneous. I presume this will come as no surprise.

	--Bob Solovay

On Wed, 5 May 2004, Randall Holmes wrote:

> Dear members of the FOM and NF mailing lists:
> if you go to my home page, http://math.boisestate.edu/~holmes
> you will find at the head of the page links to Postscript and PDF
> documents containing a draft proof that Peano arithmetic is inconsistent.
> I was inspired to work on the approach (a truth definition for PA, presented
> as a truth definition for ZF - Infinity + ~Infinity)
> by the (incorrect) proof recently proposed by Bryan Ford and advertised
> by someone else on the FOM list.  However, my proof is rather different
> from his.
> Please tell me where the mistake is if you can find one.  (also,
> please identify typos, and so forth).
> The current draft is very compact, and will be expanded and updated
> as time goes on (except in the happy case that someone can refute the
> argument!)
> Perhaps it's time to dust off our old copies of Principia Mathematica
> (the ramified theory of types is not vulnerable to this argument --
> neither is NFU + ~Inf or NFP, for NF-istes!)
> --Randall Holmes
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