Limit Models in Metric Abstract Elementary Classes: the Categorical case

TL;DR

This paper extends the theory of limit models to metric abstract elementary classes, establishing criteria for their existence and uniqueness under categoricity and superstability-like assumptions.

Contribution

It generalizes previous theorems to the metric setting, providing new criteria for limit models in this broader context.

Findings

Established criteria for existence of limit models in metric AECs

Proved uniqueness of limit models under certain assumptions

Generalized classical theorems to the metric framework

Abstract

We study versions of limit models adapted to the context of *metric abstract elementary classes*. Under categoricity and superstability-like assumptions, we generalize some theorems from [GrVaVi]. We prove criteria for existence and uniqueness of limit models in the metric context.