1Department of Mathematics, UIUC 1409 W. Green Street Urbana, IL 61801, U.S.A. 2Department of Mathematics, WIU 476 Morgan Hall, 1 University Circle Macomb, IL 61455, U.S.A.
Fundamenta Mathematicae, Tome 209 (2010) no. 2, pp. 133-155
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 $\mathop{\rm st} X\subseteq \boldsymbol k^n$.
Keywords:
answering questions kov fund math prove triangulation result independent interest detail o minimal field proper convex subring mathop boldsymbol corresponding standard part map under mild assumption definable set subseteq admits triangulation induces triangulation its standard part mathop subseteq boldsymbol
Affiliations des auteurs :
Lou van den Dries
1
;
Jana Maříková
2
1
Department of Mathematics, UIUC 1409 W. Green Street Urbana, IL 61801, U.S.A.
2
Department of Mathematics, WIU 476 Morgan Hall, 1 University Circle Macomb, IL 61455, U.S.A.
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Lou van den Dries; Jana Maříková. Triangulation in o-minimal fields with standard part map. Fundamenta Mathematicae, Tome 209 (2010) no. 2, pp. 133-155. doi: 10.4064/fm209-2-3
