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INTEGRATION AND CELL DECOMPOSITION IN P-MINIMAL STRUCTURES
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- Journal:
- The Journal of Symbolic Logic / Volume 81 / Issue 3 / September 2016
- Published online by Cambridge University Press:
- 18 July 2016, pp. 1124-1141
- Print publication:
- September 2016
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- Article
- Export citation
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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 
$\left( {K,{\cal L}} \right)$.
