A lecture for the Helsinki Logic Seminar – 30 January 2019

Slides: Around the Galois group of an AEC.

Abstract: I will provide a kind of blueprint for the study of interpretations of Abstract Elementary Classes: First, I will revisit interpretability and internality in a category-theoretical language (for first order theories, reframing work of Hrushovski and Kamensky in a formalism derived from Makkai). I will then describe the issue of recovering the biintepretability class of a theory in terms of the automorphism group of a saturated model, and the role of the “Small Index Property” (SIP). An SIP theorem for AECs with strong amalgamation properties we published with Ghadernezhad in 2018 is now placed in the context of reconstruction: I propose notions of interpretation between some specific kinds of AECs and explore the role of a Galois group for an AEC.