English

Definability and Scott rank in separable Metric structures

Logic 2024-11-05 v1

Abstract

We give a notion of Scott rank for separable metric structures based on the definability of the (metric closures of) automorphism orbits in continuous infinitary logic. This is a continuous analogue of work of Montalb\'an for countable structures. In the process, we prove some results concerning definability, type omitting, and back-and-forth for metric structures.

Keywords

Cite

@article{arxiv.2411.01017,
  title  = {Definability and Scott rank in separable Metric structures},
  author = {Diego Bejarano},
  journal= {arXiv preprint arXiv:2411.01017},
  year   = {2024}
}
R2 v1 2026-06-28T19:45:03.572Z