A (possibly new) structure without the canonical base property

TL;DR

This paper introduces a new structural property called transfer of internality on quotients, leading to the discovery of numerous new uncountably categorical additive covers of the complex numbers that lack the canonical base property.

Contribution

It generalizes the canonical base property and explores its implications for the structure of definable groups and additive covers in model theory.

Findings

Identifies a new property called transfer of internality on quotients.

Constructs infinitely many new uncountably categorical additive covers.

Shows these covers lack the canonical base property.

Abstract

In this short note, we introduce a generalization of the canonical base property, called transfer of internality on quotients. A structural study of groups definable in theories with this property yields as a consequence infinitely many new uncountably categorical additive covers of the complex numbers without the canonical base property.