# Definable sets up to definable bijections in Presburger groups

```@article{Cluckers2018DefinableSU,
title={Definable sets up to definable bijections in Presburger groups},
author={R. Cluckers and Immanuel Halupczok},
journal={arXiv: Logic},
year={2018},
volume={5},
pages={47-70}
}```
• Published 2018
• Mathematics
• arXiv: Logic
• We entirely classify definable sets up to definable bijections in \$\mathbb{Z}\$-groups, where the language is the one of ordered abelian groups. From this, we deduce, among others, a classification of definable families of bounded definable sets.
Definable combinatorics with dense linear orders
• Computer Science, Mathematics
• 2020