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INTEGRATION AND CELL DECOMPOSITION IN P-MINIMAL STRUCTURES

Published online by Cambridge University Press:  18 July 2016

PABLO CUBIDES KOVACSICS  and
EVA LEENKNEGT
PABLO CUBIDES KOVACSICS
Affiliation:
LABORATOIRE PAUL PAINLEVÉUNIVERSITÉ DE LILLE 1CNRS U.M.R. 852459655 VILLENEUVE D’ASCQ CEDEX FRANCEE-mail: [email protected]
EVA LEENKNEGT
Affiliation:
DEPARTMENT OF MATHEMATICS KULEUVEN CELESTIJNENLAAN 200B3001 HEVERLEE BELGIUME-mail: [email protected]
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Abstract

We show that the class of ${\cal L}$-constructible functions is closed under integration for any P-minimal expansion of a p-adic field $\left( {K,{\cal L}} \right)$. This generalizes results previously known for semi-algebraic and subanalytic structures. As part of the proof, we obtain a weak version of cell decomposition and function preparation for P-minimal structures, a result which is independent of the existence of Skolem functions. A direct corollary is that Denef’s results on the rationality of Poincaré series hold in any P-minimal expansion of a p-adic field $\left( {K,{\cal L}} \right)$.

Keywords

P-minimalityp-adic numbersp-adic cell decompositionconstructible functionsfunction preparationintegrationrationality of Poincaré series
Type
Articles
Information
The Journal of Symbolic Logic , Volume 81 , Issue 3 , September 2016 , pp. 1124 - 1141
Copyright
Copyright © The Association for Symbolic Logic 2016 

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