Model Theory and Differential Algebra
While I do not have lecture notes from my October 19 Kolchin seminar lectures,
there are several papers that might be of interest to you. I would be happy
to suply further references upon request.
- Introduction to Model Theory
- Introduction to Model Theory, (ps file)
Introductory Lectures in Model Theory given at MSRI for non-specialists.
- Model Theory: An Introduction :
A new introductory graduate text in model theory that has recently been
published by Springer (GTM 217). Differentially closed fields arise as
interesting examples in several places, including Poizat's treatment
of Kolchin's Galois Theory of strongly normal extensions.
- Model Theory of Differential Fields
- Model Theory of Differential Fields (ps file),
these are notes from a one hour lecture at MSRI outlining some aspects of
the model theory of differential fields. Although I gave this four years ago
it is quite similar to my lecture in the seminar.
- Model Theory of Differential Fields (ps file)
This article is based on a course I gave on
the model theory of differential fields in 1991. It appears
in the book Model Theory of Fields by Margit Messmer, Anand Pillay
and myself. A.K. Peters will shortly do a new revised printing of the book.
While this article was revised and corrected a bit, it is still based on
the 1991 lectures rather than what I might write today.
- Other references
- Manin kernels (ps file), A relatively
elementary exposition of the construction of Manin kernels and their model
- Anand Pillay's
has a number of preprints you might
find interesting including the paper
Jet spaces of varieties over differential and difference fields
with Martin Ziegler. This paper contains a rather easy proof that
nonlocally modular strongly minimal sets are closely related to the
field of constants.
- My web page, has a few other survey papers
on my other interests, including the use of model theory and fields of
logarithmic-expontential series in assymptotic differential algebra.