Notre Dame Journal of Formal Logic

Definable Open Sets As Finite Unions of Definable Open Cells

Simon Andrews


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.

Article information

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

First available in Project Euclid: 11 June 2010

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03C64: Model theory of ordered structures; o-minimality

o-minimal open cell property


Andrews, Simon. Definable Open Sets As Finite Unions of Definable Open Cells. Notre Dame J. Formal Logic 51 (2010), no. 2, 247--251. doi:10.1215/00294527-2010-015.

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