For the joint Imperial College and Queen Mary University, London, I gave the lecture

AECs and notions of existential closure.

in November 2020.

Abstract: I will provide a general overview of AECs with emphasis on their connection with various abstract notions of “existential closure”. I will present a recent joint result of myself together with Shelah (2019) on axiomatizability of AECs in infinitary logic, and examples of their interaction with closure notions. As an example, I will present aspects of a construction of a canonical “existential closure” for locally finite groups due to Shelah, and their connection with more general stability-theoretical questions.