pillay at math.uiuc.edu
Tue Oct 21 22:40:01 EDT 1997
A brief comment on Steve's manner of argument:
He quotes me:
Anand Pillay writes:
> I note that Steve and Harvey often use the expression "applied
> model theory"
> the exciting development over the last 10 years in model theory has
> been the convergence of traditions from stability theory and from
> the model theory of fields, and it is from within this new
> conceptual unity that many interesting results are arising. So I
> would prefer just "model theory".
Then he says:
"Excuse me, but I think "model theory" was created by Tarski a long
time ago. Now Anand wants to redefine "model theory" so as to make it
consist solely of stability theory and the model theory of fields.
I'm sorry, but I don't think I'll cooperate with this Putsch, at least
not until a representative group of model theorists has endorsed it.
I'll continue to say "applied model theory", until a better term is
I am surprised by Steve's apparent inability to deal with an elementary
argument involving quantifiers. Clearly the term "applied model" theory is
used in contradistinction to "pure model theory" (in fact Harvey says this
more or less explicitly in an earlier message). In my paragraph quoted
above I say that many of the recent results which Harvey and Steve consider
as "applied model theory" are actually a mixture of parts of pure model
theory (stability a la Morley,Shelah,,..) and parts of applied model theory
(model theory of fields a la Tarski, Robinson, Macintyre, van den
Dries,..), and I conclude that the term "model theory" is preferable to
"applied model theory". Somehow Steve concludes that I am defining model
theory to be "stability theory" union "model theory of fields".
As far as the supposed non basic status of the problem of rational points
on varieties goes, I just remark that Matijasevich's theorem is precisely
about integral points on varieties.
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