Around Independence and Domination in Metric Abstract Elementary Classes, under Uniqueness of Limit Models

TL;DR

This paper develops and adapts independence notions for metric abstract elementary classes, exploring their properties under superstability-like assumptions and analyzing types' domination and orthogonality when limit models are unique.

Contribution

It introduces adapted independence concepts for MAECs and examines their behavior under superstability and uniqueness of limit models, extending discrete case theories.

Findings

Independence notions behave well under superstability-like assumptions

Analysis of domination, orthogonality, and parallelism of Galois types in MAECs

Results depend on the assumption of uniqueness of limit models

Abstract

We study notions of independence appropriate for a stability theory of metric abstract elementary classes (for short, MAECs). We build on previous notions used in the discrete case, and adapt definitions to the metric case. In particular, we study notions that behave well under superstability-like assumptions. Also, under uniqueness of limit models, we study domination, orthogonality and parallelism of Galois types in MAECs.