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 st: V → k be the corresponding standard part map. Under a mild assumption on (R,V) we show that a definable set X ⊆ Vⁿ admits a triangulation that induces a triangulation of its standard part st X ⊆ kⁿ.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm209-2-3,
author = {Lou van den Dries and Jana Ma\v r\'\i kov\'a},
title = {Triangulation in o-minimal fields with standard part map},
journal = {Fundamenta Mathematicae},
volume = {209},
year = {2010},
pages = {133-155},
zbl = {1221.03030},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm209-2-3}
}
Lou van den Dries; Jana Maříková. Triangulation in o-minimal fields with standard part map. Fundamenta Mathematicae, Tome 209 (2010) pp. 133-155. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm209-2-3/