# On the interplay between Abstract Elementary Classes and Categorical Logic – Bogotá (v), 6/20

For the Seminario Flotante de Lógica Matemática de Bogotá, I gave the lecture On the interplay between Abstract Elementary Classes and Categorical Logic.

Abstract: I will describe two recent lines of interplay between Abstract Elementary Classes and Categorical Logic: the problem of building the “Galois group” of an AEC (building on Lascar and Poizat’s work on the “Galois theory of model theory”, and on the role of the Small Index Property – joint work of mine with Ghadernezhad) and interpreting $\lambda$-categoricity in terms of properties of classifying topoi (recent work of Espíndola, connected to his ground-breaking work on Shelah’s eventual categoricity conjecture). My talk will stress the way these connections appear and the opening of new lines of possibility.

# Language, Logic and Nonelementary Classes: External/Internal Interactions. Helsinki, 5/16.

A minicourse in Helsinki on Language, Logic and Nonelementary Classes: External/Internal Interactions, given at the University of Helsinki’s Mathematics Department in May of 2016.

The topics were

• Around The Presentation Theorem
• The Small Index Property for Homogeneous Classes
• Categories, AECs, Interpolation.

Here is the course material (presented on the blackboard).