A metric lifting theorem

TL;DR

This paper extends a previously established lifting theorem from the setting of reduced products of discrete structures to the broader context of metric spaces, under mild Forcing Axioms.

Contribution

It generalizes the strong lifting theorem for coordinate-respecting maps to the metric setting, broadening its applicability.

Findings

Lifting theorem successfully extended to metric spaces

Applicable under mild Forcing Axioms

Enhances understanding of maps between reduced products

Abstract

In a recent article by Farah and the authors, a strong lifting theorem was proved for a class of coordinate-respecting maps between reduced products of discrete structures, hereby working under mild Forcing Axioms. We generalise this lifting theorem to the metric setting.