Journal of Symbolic Logic 68 (1):153-162 (2003)

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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DOI 10.2178/jsl/1045861509
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References found in this work BETA

On Variants of o-Minimality.Dugald Macpherson & Charles Steinhorn - 1996 - Annals of Pure and Applied Logic 79 (2):165-209.
Quasi-o-Minimal Structures.Oleg Belegradek, Ya'acov Peterzil & Frank Wagner - 2000 - Journal of Symbolic Logic 65 (3):1115-1132.
Essentially Periodic Ordered Groups.Françoise Point & Frank O. Wagner - 2000 - Annals of Pure and Applied Logic 105 (1-3):261-291.

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