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Presburger sets and p-minimal fields

Published online by Cambridge University Press:  12 March 2014

Raf Cluckers
Raf Cluckers*
Affiliation:
Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200B, B-3001 Leuven, Belgium, E-mail: raf.cluckers@wis.kuleuven.ac.be, URL: http://www.wis.kuleuven.ac.be/algebra/raf/
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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.

Keywords

Model theoryPresburger arithmeticp-minimal fieldselimination of imaginariesZ-groups
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 68 , Issue 1 , March 2003 , pp. 153 - 162
Copyright
Copyright © Association for Symbolic Logic 2003

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