Definable Open Sets As Finite Unions of Definable Open Cells
Andrews, Simon
Notre Dame J. Formal Logic, Tome 51 (2010) no. 1, p. 247-251 / Harvested from Project Euclid
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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.
Publié le : 2010-04-15
Classification:  o-minimal,  open cell property,  03C64 
@article{1276284785,
     author = {Andrews, Simon},
     title = {Definable Open Sets As Finite Unions of Definable Open Cells},
     journal = {Notre Dame J. Formal Logic},
     volume = {51},
     number = {1},
     year = {2010},
     pages = { 247-251},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1276284785}
}

Andrews, Simon. Definable Open Sets As Finite Unions of Definable Open Cells. Notre Dame J. Formal Logic, Tome 51 (2010) no. 1, pp.  247-251. http://gdmltest.u-ga.fr/item/1276284785/