Clustered Cell Decomposition in P-Minimal Structures

Saskia Chambille; Pablo Cubides Kovacsics; Eva Leenknegt

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arXiv · 1612.02683

Clustered Cell Decomposition in P-Minimal Structures

Saskia Chambille·Pablo Cubides Kovacsics·Eva Leenknegt

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Abstract

We prove that in a $P$-minimal structure, every definable set can be partitioned as a finite union of classical cells and regular clustered cells. This is a generalization of previously known cell decomposition results by Denef and Mourgues, which were dependent on the existence of definable Skolem functions. Clustered cells have the same geometric structure as classical, Denef-type cells, but do not have a definable function as center. Instead, the center is given by a definable set whose fibers are finite unions of balls.

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BibTeX RIS

Saskia Chambille, Pablo Cubides Kovacsics, Eva Leenknegt. 2016-12-08. Clustered Cell Decomposition in P-Minimal Structures. https://arxiv.org/abs/1612.02683

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