In a 2017 paper, Ben Yaacov et. al. extended the basic ideas of Scott analysis to metric structures in infinitary continuous logic. These include back-and-forth relations, Scott sentences, and the Lopez-Escobar theorem to name a few.

In this talk, I will talk 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 Montalbán for countable structures in discrete infinitary logic. However, there are some differences arising from the subtleties behind the notion of definability in continuous logic.

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

[2] Itaï Ben Yaacov, Michal Doucha, Andre Nies, and Todor Tsankov, Metric Scott analysis, Advances in Mathematics, vol. 318 (2017), pp.46–87.

[3] Antonio Montalbán, A robuster Scott rank, Proceedings of the American Mathematical Society, vol.143 (2015), no.12, pp.5427–5436.