# Continuous logic and the strict order property

## TL;DR

This paper extends Shelah's theory to continuous logic, establishing that a continuous theory has the order property if and only if it has the independence property or the strict order property.

## Contribution

It generalizes Shelah's classical result to the setting of continuous logic, linking OP, IP, and SOP.

## Key findings

- A continuous theory has OP iff it has IP or SOP.
- The result bridges classical and continuous model theory.
- Provides a foundational understanding of order properties in continuous logic.

## Abstract

We generalize a theory of Shelah for continuous logic, namely a continuous theory has OP if and only if it has IP or SOP.