Definable Open Sets As Finite Unions of Definable Open Cells

Abstract

We introduce CE-cell decomposition, a modified version of the usual o-minimal cell decomposition. We show that if an o-minimal structure $ℛ$ admits CE-cell decomposition then any definable open set in $ℛ$ 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.