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

被引：9
|
作者：
Johnson, H. R. [1 ]
Laskowski, M. C. [2 ]
机构：
[1] CUNY, Dept Math & CS, John Jay Coll, New York, NY 10021 USA
[2] Univ Maryland, Dept Math, College Pk, MD 20742 USA
来源：
DISCRETE & COMPUTATIONAL GEOMETRY | 2010年 / 43卷 / 04期
关键词：
Compression scheme; VC dimension; NIP; Independence dimension; Dependence; Warmuth conjecture; Stable; o-minimal; Type definition; Definable type; Density; Combinatorial complexity; UFTD; UDTFS; SAMPLE COMPRESSION; DIMENSION;
D O I：
10.1007/s00454-009-9201-3
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
We show that any family of sets uniformly definable in an o-minimal 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. Extended compression schemes for uniformly definable families corresponding to stable formulas are also shown to exist.
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页码：914 / 926
页数：13
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