Towards a proof of the Shelah Presentation Theorem in Metric Abstract Elementary Classes

TL;DR

This paper proves that in Metric Abstract Elementary Classes, the new function symbols introduced in Shelah's Presentation Theorem are uniformly continuous, refining previous results that did not establish this property.

Contribution

It provides a rigorous proof that the added function symbols in the metric setting are uniformly continuous, strengthening the theoretical foundation of the theorem.

Findings

New function symbols are uniformly continuous in the metric setting

Strengthens the Shelah Presentation Theorem for Metric AECs

Clarifies the properties of added symbols in the theorem

Abstract

In my PhD thesis a version of Shelah's Presentation Theorem in the setting of Metric Abstract Elementary Classes was proved, where we claimed that the new function symbols are not necessarily uniformly continuous. In this paper we provide a proof they are in fact uniformly continuous.