Categorical Model Theory Reading Group

Accessing Shelah’s Abstract Elementary Classes.

A quest to read Christian Espindola’s paper.
Coordination: Rodrigo N. Almeida , Lingyuan Ye.


This reading group, framed as a quest to understand Espindola’s attack on Shelah’s eventual categoricty conjecture, is focused on the study of categorical model theory. The key focus for now will be on the categoricity conjecture. We will begin by exploring this setting in the more or less classical setting of classes of models of model-theoretic logics and abstract elementary classes, to understand the nature of the conjecture, before moving on to the category theoretic generalizations. Our goal will be to get a solid grounding in the kinds of tools that are used to work in this area: categorical logic; topos-theoretic completeness; infinitary completeness theorems; amongst others.

Importantly, we are not sure we will complete our quest, and that is not really the point.

Our preliminary topic schedule will be as follows:

  1. Stability Theory, Categoricity and Abstract Elementary Classes
  2. Accessible Categories and Model Theory
  3. Categorical Logic
  4. Topos Theoretic Completeness

Please contact us for access to the slack group.


Christian Espindola’s works.
Rami Grossberg, (1991) Classification Theory for Abstract Elementary Classes.
Michael Makkai, Robert Pare (1989) Accessible categories: The foundations of categorical model theory.
Michael Makkai, Gonzalo Reyes (1977) First-order categorical logic.
Saunders MacLane, Ieke Moerdijk. (1992) Sheaves in Geometry and Logic.
Jiri Adamek, Jiri Rosicky. (1999) Locally Presentable and Accessible Categories.

As of 20/10/2023, this group has been suspended. The participants have continued with the reading group with a different focus, on algebras, categories and models.

We have compiled some preliminary notes resulting from our meetings, and serving as a guide to the literature. You can find them here.

Meeting Schedule

We meet bi-weekly. Meetings are in person in SP904. We also set up hybrid participation, via this link:

Date Speaker Topic Location Time
06/02/2023 N/A Kick-Off Meeting: Introductions. Basic Motivation for the quest. Scheduling. A1.04 11h00-13h00
20/02/2023 Tibo Rushbrooke Stability Theory, Categoricity and Abstract Elementary Classes F2.01 (ILLC) 11h00-13h00
6/03/2023 Alyssa Reynaldi and Alexander Lind Accessible Categories and Model Theory F2.01 (ILLC) 11h00-13h00
20/03/2023 Davide Perinti Categorical Logic F2.01 (ILLC) 11h00-13h00
03/04/2023 Lingyuan Ye Topos Theory and Logic: Duality and Completeness F2.01 (ILLC) 11h15-13h00
17/04/2023 Jan Rooduijn Grothendieck Toposes and Classifying Toposes F2.01 (ILLC) 11h15-13h00
25/04/2023 Rodrigo Almeida Infinitary Logic: Omitting Types, Completeness and Distributive Laws F2.01 (ILLC) 11h15-13h00
15/05/2023 Jonas van der Schaaf Trees and the Transfinite Transitivity Rule F2.01 (ILLC) 11h15-13h00
05/06/2023 Daniel Otten Where we are: Categorical Logic and Topos Theory F2.01 (ILLC) 11h15-13h00
23/10/2023 Lide Grotenhuis Where we are: Infinitary Logic and the Completeness Proof F2.01 (ILLC) 11h15-13h00