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Definable open sets as finite unions of definable open cells. (English) Zbl 1208.03041
Summary: 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.

##### MSC:
 03C64 Model theory of ordered structures; o-minimality
##### Keywords:
open cell property; cell decomposition; o-minimal structure
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