[FOM] Sacks query
William Boshuck
boshuk at triples.math.mcgill.ca
Sun Nov 17 14:47:48 EST 2002
On Sat, Nov 16, 2002 at 07:45:59PM +0000, Thomas Forster wrote:
>
> Can anyone tell me (the first para at least) of a talk Sacks once
> gave (At an AMS meeting i think) which began something like
>
> ``Good afternoon, Ladies and Gentlemen. Mathematical
> Logic
It's from: The differential closure of a differential
field, Bulletin of the AMS 78 No.5 (1972), 629-634.
Here's the first paragraph:
``Good afternoon ladies and gentlemen. The subject of
mathematical logic splits fourfold into: recursive
functions, the heart of the subject; proof theory,
which includes the best theorem in the subject; sets
and classes, whose romantic appeal far outweigh their
mathematical substance; and model theory, whose value
is its applicability to, and roots in, algebra. This
afternoon I hope to sketch some theorems about
differential fields first derived by model theoretic
methods. In particular, I will indicate why every
differential field A of characteristic 0 has a unique
prime differentially closed extension called the
differential closure of A. Model theory has proved
usefule in the study of diferential fields because the
notion of differential closure is surprisingly more
complex than the analogous notions of algebraic
closure, real closure, or Henselization. The virtue of
model theory is its ability to organize succinctly the
sort of tiresome algebraic details associated with
elimination theory.''
cheers,
-b
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