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:
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.
We have compiled some preliminary notes resulting from our meetings, and serving as a guide to the literature. You can find them here.
We meet bi-weekly. Meetings are in person in SP904. We also set up hybrid participation, via this link:
|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|