The Canonical Base Property and CM-Triviality

Explore a 27-minute lecture from the Workshop on Trends in Pure and Applied Model Theory, presented by Léo Jimenez at the Fields Institute. Delve into the concepts of the canonical base property and CM-triviality, starting with an introduction and setup. Examine internality and the generalization of one-basedness through the Canonical Base Property. Investigate the first counterexample and its essential features, considering the possibility of other counterexamples. Learn about CM-triviality as a method to avoid interpreting a field, and study finite dimensional Lie algebras. Analyze the delta function and its class, along with amalgamation and collapse. Follow two proof sketches: one on derivations and automorphisms, and another on constructing derivations. Conclude with a discussion of further questions in this area of model theory.

Intro
Setup
Internality
Generalizing one-basedness: the Canonical Base Property
The first counterexample
Essential features of the counterexample
What about other counterexamples?
How to not interpret a field: CM-triviality
Finite dimensional Lie algebras
Delta function and the class
Amalgamation and Collapse
Proof Sketch 1: Derivations and automorphisms
Proof Sketch 2: Constructing Derivations
Further Questions