During the event Logic, Categories and Philosophy of Mathematics – In celebration of Michael Makkai’s 80th Birthday, I gave the lecture
Abstract Elementary Classes and their Galois groups: Interpretations Revisited.
Abstract: We study interpretations in Abstract Elementary Classes. We recast notions of interpretability and internality (following Hrushovski and Kamensky who based their work on earlier results due to Makkai and Reyes) and their version of a model theoretic Galois theory. We present results for AECs that satisfy a Small Index Property (enabling one to recover the biinterpretability class of theories) and on the Galois groups of those AECs. We stress the role of the Presentation Theorem and of a recent logic due to Shelah that enables us to define AECs.