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

H. R. Johnson, M. C. Laskowski
<span title="2009-06-18">2009</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="" style="color: black;">Discrete &amp; Computational Geometry</a> </i> &nbsp;
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 * † Partially supported by NSF grant DMS-0600217. definable family in a structure with a o-minimal theory is bounded by the number of parameters in the defining formula. Extended compression schemes for uniformly definable
more &raquo; ... s corresponding to stable formulas are also shown to exist.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="">doi:10.1007/s00454-009-9201-3</a> <a target="_blank" rel="external noopener" href="">fatcat:44jjhnaajren5hxl7ijffrieie</a> </span>
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