Compression Schemes, Stable Definable Families, and o-Minimal Structures

@article{Johnson2010CompressionSS,
  title={Compression Schemes, Stable Definable Families, and o-Minimal Structures},
  author={H. R. Johnson and Michael C. Laskowski},
  journal={Discrete & Computational Geometry},
  year={2010},
  volume={43},
  pages={914-926}
}
We show that any family of sets uniformly definable in an ominimal structure has an extended compression scheme of size equal to the number of parameters in the defining formula. As a consequence, the combinatorial complexity (or density) of any definable family in a structure with a o-minimal theory is bounded by the number of parameters in the defining formula. ∗Partially supported by NSF grant DMS-0600217. 

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References

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Showing 1-10 of 15 references

Model Theory and Exponentiation

View 2 Excerpts
Highly Influenced

Model Theory: An Introduction

D. Marker
Springer, New York • 2002

Tame Topology and O-minimal Structures, Number 248 in London Mathematical Society Lecture Notes Series

L. van den Dries
1998
View 2 Excerpts

Geometric Stability Theory

A. Pillay
Oxford University Press • 1996

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