# Presburger sets and p-minimal fields

@article{Cluckers2003PresburgerSA, title={Presburger sets and p-minimal fields}, author={R. Cluckers}, journal={Journal of Symbolic Logic}, year={2003}, volume={68}, pages={153 - 162} }

Abstract We prove a cell decomposition theorem for Presburger sets and introduce a dimension theory for Z-groups with the Presburger structure. Using the cell decomposition theorem we obtain a full classification of Presburger sets up to definable bijection. We also exhibit a tight connection between the definable sets in an arbitrary p-minimal field and Presburger sets in its value group. We give a negative result about expansions of Presburger structures and prove uniform elimination of… Expand

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#### 56 Citations

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