On many-sorted $\omega$-categorical theories

TL;DR

This paper demonstrates that all many-sorted ω-categorical theories can be interpreted in one-sorted ω-categorical theories, and uses this to show the existence of non G-compact ω-categorical theories.

Contribution

It proves interpretability of many-sorted ω-categorical theories in one-sorted ones, providing new insights into their structure and properties.

Findings

Every many-sorted ω-categorical theory is interpretable in a one-sorted ω-categorical theory.

The existence of non G-compact ω-categorical theories is established.

A short proof of non G-compactness in ω-categorical theories is provided.

Abstract

We prove that every many-sorted $\omega$-categorical theory is completely interpretable in a one-sorted $\omega$-categorical theory. As an application, we give a short proof of the existence of non $G$--compact $\omega$-categorical theories.