Integration and Cell Decomposition in $P$-minimal Structures

Pablo Cubides Kovacsics; Eva Leenknegt

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arXiv · 1502.06467

Integration and Cell Decomposition in $P$-minimal Structures

Pablo Cubides Kovacsics·Eva Leenknegt

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Abstract

We show that the class of $\mathcal{L}$-constructible functions is closed under integration for any $P$-minimal expansion of a $p$-adic field $(K,\mathcal{L})$. 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 Poincar\'e series hold in any $P$-minimal expansion of a $p$-adic field $(K,\mathcal{L})$.

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BibTeX RIS

Pablo Cubides Kovacsics, Eva Leenknegt. 2015-02-23. Integration and Cell Decomposition in $P$-minimal Structures. https://arxiv.org/abs/1502.06467

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