__Lecturer:__ Rami Grossberg
MWF 2:30, BH 231A.

This will be a new course.

Part of the course will be set theoretic in nature:
The fundamentals of shelah ''non-structure'' theory will be presented,
which are also the roots of
*proper forcing*
and
*pcf
theory*.

The other part is structure theory (more like commutative algebra): The main results to be discussed are orthogonality calculus, and the structure of regular types. This will be used to prove to Shelah's "Main Gap Theorem" for countable theories. If time will permit I will discuss also the solution to Morley's conjecture (i.e. the mapping lÆ I(l,T) is a weakly monotonic). Probably will also make comments on the lower part of the spectrum function.

It is expected that the students know elementary set theory
as well as the
fundamentals of classification theory (including various equivalent
properties to superstability, forking calculus, and the stability
spectrum theorem).

__Prerequisites:__ Little more than an
elementary course in model theory (21-603) and
a graduate course in algebra or permission of the
instructor.
The most basic parts of
the primer to simple
theories and some elementary properties of rank functions
www.math.cmu.edu/~rami/DR.dvi

__Books:__ There is no official text, the following
is the most relevant:

Saharon Shelah,
**Classification Theory
and the Number of Nonisomorphic Models**, Rev. Ed.,
North-Holland, 1990, Amsterdam.
price comparison.

File translated from T

On 19 Apr 2000, 10:41.