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From: ladkin@kestrel.ARPA
Newsgroups: net.math
Subject: Re: Godel-Escher-Bach ans. + new problem
Message-ID: <4586@kestrel.ARPA>
Date: Wed, 5-Feb-86 15:09:35 EST
Article-I.D.: kestrel.4586
Posted: Wed Feb  5 15:09:35 1986
Date-Received: Fri, 7-Feb-86 20:52:27 EST
References: <139800001@uoregon.UUCP> <139800002@uoregon.UUCP>
Organization: Kestrel Institute, Palo Alto, CA
Lines: 17

In article <139800002@uoregon.UUCP>, luks@uoregon.UUCP (luks) writes:
> [...]  A significant result of mathematical logic
> is the observation that a first-order theory based only upon Peano's
> Postulates seems to incorporate all the basic statements and proofs
> of elementary number theory.  See, for example, Chapter 3 of
> [Introduction to Mathematical Logic, by Elliott Mendelson,
> Van Nostrand, 1964]

No longer true. Paris and Harrington have a formulation of
Ramsey's Theorem which is unprovable in Peano Arithmetic
(see Handbook of Mathematical Logic, North-Holland 1977),
and much work along the same lines has been done by,
particularly, Harvey Friedman (e.g. Kruskal's Theorem
is unprovable in Peano Arithmetic). 
*Result* is an unfortunate choice of words.

Peter Ladkin