Courses:

This is an advanced topics course in model theory whose main theme is simple theories. We treat simple theories in the framework of compact abstract theories, which is more general than that of first order theories. We cover the basic properties of independence (i.e., non-dividing) in simple theories, the characterisation of simple theories by the existence of a notion of independence, and hyperimaginary canonical bases.

Other topics covered include stability as a special case of simplicity, adding a generic automorphism to a stable first order theory, definable groups in simple theories and lovely pairs.

The Topics in detail are listed below:

• Universal domains for compact abstract theories
• Indiscernibility and extraction of indiscernible sequences
• Dividing, simplicity, and independence
• Lascar strong types and the independence theorem
• Characterisation of simplicity and through abstract notion of independence
• Hyperimaginaries and canonical bases
• Supersimplicity and the Lascar inequalities
• Connection between simplicity and stability
• Stable theories with a generic automorphism
• Type-definable groups
• Lovely pairs
  

Prerequisites

A basic graduate course in model theory (18.575 or equivalent).

Grading

The course grades will be based on general participation and lectures given by the students.