**Instructor**: Rami Grossberg

**Office**: WEH 7204

**Phone**: x8482 (268-8482 from external lines), messages at
x2545

**Email**: Rami@cmu.edu

**URL**:
www.math.cmu.edu/~rami

**Office Hours:** By appointment or whenever else you can
find me.

**Purpose**. This is a second course in model theory. The main
topic of discussion will be classification theory for non-elemntary classes.

**Course description**.

I will concentrate in what is
the deepest part of pure model theory. Namely non-first order
theories. We will focus in abstract elementary classes.
An AEC is
a class K of models all of the same similarity type (or a category of
sets) with a notion of an embedding
which is closed under direct limits and little more. The aim is to have
an analysis of such general classes. Most of the material
to be discussed appears in (badly written) papers only.
I will start with minimal prerequisits, but will progress quickly to some
of the research frontieers of the field.
I will
concentrate in parts of the
the theory that may eventually converge to a proof cases of Shelah's
categoricity
conjecture which is the prominent open problem in the field, it is
a
parallel to
Morley's theorem for L_{w1,w}, most results will be about
more general classes. The common to all these classes is that the
compactness theorem fails badly. Hopefully some of the techniques will
turn to be usefull also in the study of classes of finite models, but we
will concentrate at infinite models.
There will be a more serious use of set theory
than needed for model theory of first-order logic.

__Prerequisites:__ About half of a basic graduate course in set
theory and parts of an
elementary model theory course (about 60-70% of
21-603) or permission of the instructor.

__Textbook:__ There is no official text.

Material for students in this course, if you use this link you agree not to forward and/or share the contents without my explicit agreement.

Rami's home page.

Last modified:
September 9^{th}, 2004 |