Presburger sets and p-minimal fields

2002/06/19 by Raf Cluckers
Mathematics · #math.LO #msc:03C07

paper · pdf

published as J. Symbolic Logic 68 (2003), 153--162 · to appear in the Journal of Symbolic Logic

arxiv created 2002/06/19 · arxiv updated 2009/11/30

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 imaginaries for Presburger structures within the Presburger language.

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