[FOM] inconsistency of PA

Randall Holmes holmes at diamond.boisestate.edu
Wed May 5 16:30:44 EDT 2004

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

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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