# Continuous Sentences Preserved Under Reduced Products

## TL;DR

This paper characterizes which continuous sentences remain true when taking reduced products of metric structures, extending the analysis to a broader class of structures.

## Contribution

It provides a syntactic characterization of continuous sentences preserved under reduced products, answering a question posed by Cifu Lopes and generalizing to broader structures.

## Key findings

- Identifies conditions for sentences preserved under reduced products
- Extends results to general structures beyond metric structures
- Provides a syntactic criterion for preservation

## Abstract

Answering a question of Cif\'u Lopes, we give a syntactic characterization of those continuous sentences that are preserved under reduced products of metric structures. In fact, we settle this question in the wider context of general structures as introduced by the second author.