Diego Bejarano, York University
Definability and Scott rank in separable metric structures
In [2], 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 on 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 more robust Scott rank developed by Montalbán in [3] 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.
MC 5417