Triangulation in o-minimal fields with standard part map

Lou Den Van Dries; Jana Maříková

doi:10.4064/fm209-2-3

Triangulation in o-minimal fields with standard part map

Lou Den Van Dries, Jana Maříková

Research output: Contribution to journal › Article › peer-review

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 st : V → κ 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 ⊆ κⁿ.

Original language	English (US)
Pages (from-to)	133-155
Number of pages	23
Journal	Fundamenta Mathematicae
Volume	209
Issue number	2
DOIs	https://doi.org/10.4064/fm209-2-3
State	Published - 2010
Externally published	Yes

Keywords

O-minimal structures
Residue field
Triangulation

ASJC Scopus subject areas

Algebra and Number Theory

Online availability

10.4064/fm209-2-3

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AB - 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 → κ 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 ⊆ κn.

KW - O-minimal structures

KW - Residue field

KW - Triangulation

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Triangulation in o-minimal fields with standard part map

Abstract

Keywords

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