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}
}
  • R. Cluckers, Immanuel Halupczok
  • 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

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 16 REFERENCES
    Presburger sets and p-minimal fields
    • 48
    • PDF
    Classification of semi-algebraic $p$-adic sets up to semi-algebraic bijection
    • 24
    • PDF
    Integration in valued fields
    • 122
    • PDF
    Grothendieck rings of o-minimal expansions of ordered abelian groups
    • 10
    • PDF
    Constructible motivic functions and motivic integration
    • 134
    • PDF
    Tame Topology and O-Minimal Structures
    • 636
    Model theory : an introduction
    • 683
    • PDF
    There are no Intermediate Structures between the Group of Integers and Presburger Arithmetic
    • 15
    • PDF
    The Value Ring of Geometric Motivic Integration, and the Iwahori Hecke Algebra of SL2
    • 22
    • Highly Influential
    • PDF