Notre Dame Journal of Formal Logic

Definable Open Sets As Finite Unions of Definable Open Cells

Simon Andrews

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

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

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

Dates
First available in Project Euclid: 11 June 2010

Permanent link to this document
http://projecteuclid.org/euclid.ndjfl/1276284785

Digital Object Identifier
doi:10.1215/00294527-2010-015

Zentralblatt MATH identifier
05758440

Mathematical Reviews number (MathSciNet)
MR2667935

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

Keywords
o-minimal open cell property

Citation

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. http://projecteuclid.org/euclid.ndjfl/1276284785.


Export citation

References

  • [1] van den Dries, L., Tame Topology and O-Minimal Structures, vol. 248 of London Mathematical Society Lecture Note Series, Cambridge University Press, Cambridge, 1998.
  • [2] Edmundo, M., "Coverings by open cells in nonlinear o-minimal expansions of groups", Preprint, 2008.
  • [3] Peterzil, Y., and S. Starchenko, "A trichotomy theorem for o-minimal structures", Proceedings of the London Mathematical Society. Third Series, vol. 77 (1998), pp. 481--523.
  • [4] Wilkie, A., "Covering definable open sets by open cells", in Proceedings of the RAAG Summer School Lisbon 2003: O-minimal Structures, edited by M. Edmundo, D. Richardson, and A. J. Wilkie, RAAG, Lisbon. 2005.