Date/Time
Date(s) - 02/02/2026
12:30 pm - 1:30 pm

Speaker: Diego Bejarano (York University)

Location: Hamilton Hall, Room 410

Title: Definability and Scott rank in separable metric structures

Abstract: In \cite{ben17}, Ben Yaacov et. al. extended the basic ideas of Scott analysis to metric structures in infinitary continuous logic. These ideas include back-and-forth relations, Scott sentences, and the Lopez-Escobar theorem to name a few. In this talk, I will talk about my work connecting the ideas of Scott analysis to the definability of automorphism orbits and a notion of isolation for types within separable metric structures. Our results are a continuous analogue of the robuster Scott rank developed by Montalb\’an in \cite{mon15} for countable structures in discrete infinitary logic. However, there are some differences arising from the subtleties behind the notion of definability in continuous logic.

Diego Bejarano, Definability and Scott rank in separable metric structures, https://arxiv.org/abs/2411.01017

[ben17]  Ita{\”\i}~Ben Yaacov, Michal Doucha, Andre Nies, and Todor Tsankov, Metric Scott analysis,
Advances in Mathematics, vol. 318 (2017), pp.46–87.

[mon15] Antonio Montalb{\’a}n,
A robuster Scott rank, Proceedings of the American Mathematical Society,
vol.143 (2015), no.12, pp.5427–5436.