Triangulation in o-minimal fields with standard part map
Volume 209 / 2010
Fundamenta Mathematicae 209 (2010), 133-155
MSC: 03C64, 14P10.
DOI: 10.4064/fm209-2-3
Abstract
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 $\mathop{\rm st} X\subseteq \boldsymbol k^n$.
