Reduction of semialgebraic constructible functions

Ludwig Bröcker. "Reduction of semialgebraic constructible functions." Annales Polonici Mathematici 87.1 (2005): 27-38. <http://eudml.org/doc/281084>.

@article{LudwigBröcker2005,
abstract = {Let R be a real closed field with a real valuation v. A ℤ-valued semialgebraic function on Rⁿ is called algebraic if it can be written as the sign of a symmetric bilinear form over R[X₁,. .., Xₙ]. We show that the reduction of such a function with respect to v is again algebraic on the residue field. This implies a corresponding result for limits of algebraic functions in definable families.},
author = {Ludwig Bröcker},
journal = {Annales Polonici Mathematici},
keywords = {limits of semialgebraic functions; reduction with respect to a valuation; Euler integral},
language = {eng},
number = {1},
pages = {27-38},
title = {Reduction of semialgebraic constructible functions},
url = {http://eudml.org/doc/281084},
volume = {87},
year = {2005},
}

TY - JOUR
AU - Ludwig Bröcker
TI - Reduction of semialgebraic constructible functions
JO - Annales Polonici Mathematici
PY - 2005
VL - 87
IS - 1
SP - 27
EP - 38
AB - Let R be a real closed field with a real valuation v. A ℤ-valued semialgebraic function on Rⁿ is called algebraic if it can be written as the sign of a symmetric bilinear form over R[X₁,. .., Xₙ]. We show that the reduction of such a function with respect to v is again algebraic on the residue field. This implies a corresponding result for limits of algebraic functions in definable families.
LA - eng
KW - limits of semialgebraic functions; reduction with respect to a valuation; Euler integral
UR - http://eudml.org/doc/281084
ER -