### Definable Open Sets As Finite Unions of Definable Open Cells

Simon Andrews
Source: Notre Dame J. Formal Logic Volume 51, Number 2 (2010), 247-251.

#### Abstract

We introduce CE-cell decomposition, a modified version of the usual o-minimal cell decomposition. We show that if an o-minimal structure $\mathcal{R}$ admits CE-cell decomposition then any definable open set in $\mathcal{R}$ may be expressed as a finite union of definable open cells. The dense linear ordering and linear o-minimal expansions of ordered abelian groups are examples of such structures.

First Page:
Primary Subjects: 03C64
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Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1276284785
Digital Object Identifier: doi:10.1215/00294527-2010-015
Zentralblatt MATH identifier: 05758440
Mathematical Reviews number (MathSciNet): MR2667935

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