INTEGRATION AND CELL DECOMPOSITION IN P-MINIMAL STRUCTURES

被引：6

作者：

Kovacsics, Pablo Cubides ^{[1
]}

Leenknegt, Eva ^{[2
]}

机构：

[1] Univ Lille 1, Lab Paul Painleve, CNRS UMR 8524, F-59655 Villeneuve Dascq, France

[2] KULeuven, Dept Math, Celestijnenlaan 200B, B-3001 Heverlee, Belgium

来源：

JOURNAL OF SYMBOLIC LOGIC | 2016年 / 81卷 / 03期

基金：

欧洲研究理事会;

关键词：

P-minimality; p-adic numbers; p-adic cell decomposition; constructible functions; function preparation; integration; rationality of Poincare series; FIELDS; SETS; VERSION;

D O I：

10.1017/jsl.2015.38

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 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 Poincare series hold in any P-minimal expansion of a p-adic field (K, L).

引用

页码：1124 / 1141

页数：18

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