Definability and Isomorphisms 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 my work connecting
the ideas of Scott analysis to the definability of (closures of)
automorphism orbits and a notion of isolation for certain partial
types within separable metric structures.
These results are a continuous analogue of the robuster Scott rank
developed by Montalban in [1] for countable structures in discrete
infinitary logic. However, there are some notable differences that
arise from the subtleties behind definability in continuous logic.
[1] Antonio Montalban. A robuster Scott rank. Proceedings of the American Mathematical Society, 143(12):5427--5436, April 2015.
[2] Itaï Ben Yaacov, Michal Doucha, Andre Nies, and Todor Tsankov.
Metric Scott analysis. 318:46--87, 2017.
