Clustered Cell Decomposition in P-Minimal Structures
Year: 2016
Type: preprint
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.
Source: arXiv (Cornell University)
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Vlaamse regering
OpenAlex ID: W2950818994