Integration and Cell Decomposition in P-minimal Structures

2015/02/23 by Pablo Cubides Kovacsics, Kovacsics, Pablo Cubides, Eva Leenknegt +1
Mathematics · #03c10 #03c64 #11u09. Secondary: 03c07 #FOS: Mathematics #Logic (math.LO) #Number Theory (math.NT) #Primary: 12J12 #math.LO #math.NT #msc:03c07 #msc:03c10 #msc:03c64 #msc:11u09. #msc:12J12

paper · pdf · doi:10.48550/arxiv.1502.06467

22 pages

arxiv created 2015/02/23 · arxiv updated 2015/02/24

Abstract

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).

Related

• Cell Decomposition for semibounded p-adic sets
• Cell decomposition and definable functions for weak p-adic structures
• Exponential-constructible functions in P-minimal structures
• Cell decomposition and p-adic integration
• Differentiation in P-minimal structures and a p-adic Local Monotonicity Theorem