Reduction of semialgebraic constructible functions
Volume 87 / 2005
Annales Polonici Mathematici 87 (2005), 27-38
MSC: 14P10, 12J25, 28A25.
DOI: 10.4064/ap87-0-3
Abstract
Let $ R $ be a real closed field with a real valuation $v$. A $ {\Bbb{Z}} $-valued semialgebraic function on $R^n$ is called algebraic if it can be written as the sign of a symmetric bilinear form over $R [X_1, \ldots , X_n]$. 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.
