From: Peter Percival Subject: Re: My unprovability madness. Date: Fri, 08 Sep 2000 21:10:25 +0100 Newsgroups: sci.math Summary: [missing] Nicolas Bray wrote: > > On Sun, 20 Aug 2000, Mike Oliver wrote: > > > Peter Percival wrote: > > > > > What about Paris? > > > > Ah yes. We'll always have Paris. > > Shouldn't that be, "We'll always have Paris, Harrington."? > > (Darn, I should have said that to him at the end of my class with him last > semester.) Sorry, if I was unhistorical in mentioning only Paris... "The first examples of strictly mathematical statements about natural numbers which are true but not provable in PA (Peano Arithmetic) were due to the first author (see Paris [2], and grew out of the work in Paris and Kirby [1]. The second author's contribution was to show that Paris's proof could be carried through with the particularly simple extension of the Finite Ramsey Theorem..." [3] [1] L.Kirby, J.Paris. Initial segments of models of Peano's axioms. "Proceedings of the Bierutowice Conference 1976", Springer, Berlin, 1979 [2] J.Paris. Independence results for Peano arithmetic. "J. Symbolic Logic", 1978, vol.43, N4, pp.725-731 [3] J.Paris, L.Harrington. A mathematical incompleteness in Peano arithmetic. In Barwise [4]. [4] J. Barwise. Handbook of Mathematical Logic, Elsevier Science Ltd., 1977 -- The From: address in the header is fictional I am peter dot percival at cwcom dot net