# 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} }

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.

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