On the small index property for AECs with strong amalgamation properties

Abstract: We first revisit notions of interpretability and internality in a category-theoretical language (for first order theories), reframing work of Hrushovski and Kamensky in a formalism derived from Makkai's early work. We then describe the issue of recovering the bi-intepretability class of a theory in terms of the automorphism group of a saturated model, and the role of the "Small Index Property" (SIP) - a way of recovering the topology of a group action from purely algebraic information.

We then turn to abstract elementary classes, and discuss the same notions, in the opposite order: first, two situations where a Small Index Property holds (joint work with Ghadernezhad), and then some applications to the problem of interpretation and reconstruction, adapted to abstract elementary classes.

computational complexitycategory theorylogic

Audience: researchers in the topic

PALS Panglobal Algebra and Logic Seminar

Series comments: The PALS seminar is a research and learning seminar organized by the algebra and logic research group of the Department of Mathematics at the University of Colorado at Boulder. The scope of the seminar includes all topics with links to algebra, logic, or their applications, like general algebra, logic, model theory, category theory, set theory, set-theoretic topology, or theoretical computer science. Please contact one of the organizers for the Zoom password, to join the mailing list or if you want to speak.