Rami Grossberg (rami@cmu.edu)

MWF 2:30

PH 125B

12 Units

I will introduce Shelah's notion of dependence in model theory namely the forking relation. It will be developed in the most general context of simple theories (See my paper with Iovino and Lessmann). It will be used to prove uniqueness of prime models for stable theories, thus answering a 30 year old conjecture of Ritt concerning the uniqueness of differential closure. The finite equivalence relation theorem, the stability spectrum theorem, unions of saturated models is saturated (under sufficent stablty). Several extensions of these ideas will be discussed.