O-minimal fields with standard part map

Jana Maříková. "O-minimal fields with standard part map." Fundamenta Mathematicae 209.2 (2010): 115-132. <http://eudml.org/doc/283337>.

@article{JanaMaříková2010,
abstract = {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 $k_\{ind\}$ be the expansion of k by the standard parts of the definable relations in R. We investigate the definable sets in $k_\{ind\}$ and conditions on (R,V) which imply o-minimality of $k_\{ind\}$. We also show that if R is ω-saturated and V is the convex hull of ℚ in R, then the sets definable in $k_\{ind\}$ are exactly the standard parts of the sets definable in (R,V).},
author = {Jana Maříková},
journal = {Fundamenta Mathematicae},
keywords = {o-minimal structures; residue field},
language = {eng},
number = {2},
pages = {115-132},
title = {O-minimal fields with standard part map},
url = {http://eudml.org/doc/283337},
volume = {209},
year = {2010},
}

TY - JOUR
AU - Jana Maříková
TI - O-minimal fields with standard part map
JO - Fundamenta Mathematicae
PY - 2010
VL - 209
IS - 2
SP - 115
EP - 132
AB - 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 $k_{ind}$ be the expansion of k by the standard parts of the definable relations in R. We investigate the definable sets in $k_{ind}$ and conditions on (R,V) which imply o-minimality of $k_{ind}$. We also show that if R is ω-saturated and V is the convex hull of ℚ in R, then the sets definable in $k_{ind}$ are exactly the standard parts of the sets definable in (R,V).
LA - eng
KW - o-minimal structures; residue field
UR - http://eudml.org/doc/283337
ER -