O-minimal fields with standard part map

Jana Maříková

Fundamenta Mathematicae, Tome 209 (2010), p. 115-132 / Harvested from The Polish Digital Mathematics Library

Résumé

Let R be an o-minimal field and V a proper convex subring with residue field k and standard part (residue) map st: V → k. Let $k_{i n d}$ be the expansion of k by the standard parts of the definable relations in R. We investigate the definable sets in $k_{i n d}$ and conditions on (R,V) which imply o-minimality of $k_{i n d}$ . We also show that if R is ω-saturated and V is the convex hull of ℚ in R, then the sets definable in $k_{i n d}$ are exactly the standard parts of the sets definable in (R,V).

Publié le : 2010-01-01

Zbl 1221.03029

EUDML-ID : urn:eudml:doc:283337

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     author = {Jana Ma\v r\'\i kov\'a},
     title = {O-minimal fields with standard part map},
     journal = {Fundamenta Mathematicae},
     volume = {209},
     year = {2010},
     pages = {115-132},
     zbl = {1221.03029},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm209-2-2}
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Jana Maříková. O-minimal fields with standard part map. Fundamenta Mathematicae, Tome 209 (2010) pp. 115-132. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm209-2-2/