One Lie group to define them all

TL;DR

This paper constructs a connected real Lie group capable of interpreting the real field with integers, with the interpretation domain definable within the group, bridging Lie theory and model theory.

Contribution

It introduces a novel connected real Lie group that interprets an expanded real field, linking Lie groups with number-theoretic structures in model theory.

Findings

The Lie group interprets the real field with integers.

The interpretation domain is definable within the group.

This bridges Lie theory and model-theoretic interpretability.

Abstract

We produce a connected real Lie group that, as a first order structure in the group language, interprets the real field expanded with a predicate for the integers. Moreover, the domain of our interpretation is definable in the group.