Triangulation in o-minimal fields with standard part map

Volume 209 / 2010

Lou van den Dries, Jana Maříková Fundamenta Mathematicae 209 (2010), 133-155 MSC: 03C64, 14P10. DOI: 10.4064/fm209-2-3


In answering questions of J. Maříková [Fund. Math. 209 (2010)] we prove a triangulation result that is of independent interest. In more detail, let $R$ be an o-minimal field with a proper convex subring $V$, and let $\mathop{\rm st}: V \to \boldsymbol k$ be the corresponding standard part map. Under a mild assumption on $(R,V)$ we show that a definable set $X\subseteq V^n$ admits a triangulation that induces a triangulation of its standard part $\mathop{\rm st} X\subseteq \boldsymbol k^n$.


  • Lou van den DriesDepartment of Mathematics, UIUC
    1409 W. Green Street
    Urbana, IL 61801, U.S.A.
  • Jana MaříkováDepartment of Mathematics, WIU
    476 Morgan Hall, 1 University Circle
    Macomb, IL 61455, U.S.A.

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