Submission date: 8 December 2016

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.

Mathematics Subject Classification: 03C10, 12J12, 12J25

Keywords and phrases:

Full text arXiv 1612.02683: pdf, ps.