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
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
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.