# Uniform local definable cell decomposition for locally o-minimal expansion of the group of reals

@article{Fujita2019UniformLD, title={Uniform local definable cell decomposition for locally o-minimal expansion of the group of reals}, author={M. Fujita}, journal={arXiv: Logic}, year={2019} }

We demonstrate the following uniform local definable cell decomposition theorem in this paper.
Consider a structure $\mathcal M = (M, <,0,+, \ldots)$ elementarily equivalent to a locally o-minimal expansion of the group of reals $(\mathbb R, <,0,+)$. Let $\{A_\lambda\}_{\lambda\in\Lambda}$ be a finite family of definable subsets of $M^{m+n}$. There exist an open box $B$ in $M^n$ containing the origin and a finite partition of definable sets $M^m \times B = X_1 \cup \ldots \cup X_k$ such that… Expand

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