Reconstruction of separably categorical metric structures

TL;DR

This paper extends classical reconstruction results to metric structures, demonstrating that separably categorical metric structures are uniquely determined by their automorphism groups up to bi-interpretability.

Contribution

It generalizes Ahlbrandt and Ziegler's results from classical to metric structures, establishing a bi-interpretability classification based on automorphism groups.

Findings

Separable categoricity implies automorphism group determines the structure.

Extension of classical reconstruction results to metric structures.

Automorphism groups classify structures up to bi-interpretability.

Abstract

We extend Ahlbrandt and Ziegler's reconstruction results to the metric setting: we show that separably categorical metric structures are determined, up to bi-interpretability, by their automorphism groups.