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

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. 1 

• Type: Journal
• Year: 2010
• Where: DCG
• Authors: H. R. Johnson, M. C. Laskowski
• Keywords: Computer Graphics, DCG 2010, Definable Family, Extended Compression Scheme, Nsf Grant Dms-0600217