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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
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