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Preprint Number 838
838. Pablo Cubides Kovacsics, Eva Leenknegt
Integration and Cell Decomposition in P-minimal Structures
Submission date: 23 February 2015.
We show that the class of L-constructible functions is closed under integration for any P-minimal expansion of a p-adic field (K,L). This generalizes results previously known for semi-algebraic and sub-analytic 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. The result is obtained from weak versions of cell decomposition and function preparation which we prove for general P-minimal structures. 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 (K,L).
Mathematics Subject Classification: 12J12, 03c10, 11u09. Secondary: 03c07, 03c64
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