# Groups definable in Presburger arithmetic

## TL;DR

This paper classifies all groups that can be defined within Presburger arithmetic, providing a comprehensive understanding of their structure up to finite index subgroups.

## Contribution

It offers a complete classification of definable groups in Presburger arithmetic, a significant step in understanding its model-theoretic properties.

## Key findings

- All definable groups are virtually abelian.
- Classification up to finite index subgroups.
- Provides a structural description of these groups.

## Abstract

We determine all groups definable in Presburger arithmetic, up to a finite index subgroup.