21-703 21-703     Model Theory II - The spectrum function

Lecturer: Rami Grossberg MWF 2:30, BH 231A.

Course description

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 l 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 TEX by TTH, version 2.25.
On 19 Apr 2000, 10:41.