Definable Open Sets As Finite Unions of Definable Open Cells

Notre Dame Journal of Formal Logic 51 (2):247-251 (2010)
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
Keywords o-minimal   open cell property
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DOI 10.1215/00294527-2010-015
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CE-Cell Decomposition and Open Cell Property in o-Minimal Structures.Tari Somayyeh - 2017 - Annals of Pure and Applied Logic 168 (8):1564-1570.

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