18.996A | Spring 2004 | Graduate

Simplicity Theory

Lecture Notes

The handwritten lecture notes are provided courtesy Christina Goddard, a student in the class. Used with permission.

1 The Basic Setting: Universal Domains (PDF)
2 Extraction of Indiscernible Sequences
(Taught by David K. Milovich)
3 Dividing and its Basic Properties (PDF)
4 Simplicity

Statement of the Properties of Independence

Morley Sequences

Proof of Symmetry and Transitivity from Extension

5 Thickness

Total D-rank and Extension

6 Lascar Strong Types and the Independence Theorem
(Partially taught by Christina Goddard)
7 Examples: Hilbert Spaces, Hyperimaginary Sorts
(Taught by Josh Nichols-Barrer)
8 Generically Transitive Relations

Amalgamation Bases, Parallelism and Canonical Bases

9 Characterisation of Simplicity and Non-dividing in Terms of Abstract Notion of Independence
(Taught by Cameron Freer)
10 Supersimplicity

Lascar Inequalities


11-12 Stable Theories with a Generic Automorphism (PDF)
13-14 Groups: Stratified Ranks, Generic Elements and Types

Connected Components, Stabilisers

15-16 Lovely Pairs (PDF)

Course Info

As Taught In
Spring 2004
Learning Resource Types
Lecture Notes
Problem Sets