Reduction of semialgebraic constructible functions

Volume 87 / 2005

Ludwig Bröcker Annales Polonici Mathematici 87 (2005), 27-38 MSC: 14P10, 12J25, 28A25. DOI: 10.4064/ap87-0-3


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.


  • Ludwig BröckerMathematisches Institut
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    D-48149 Münster, Germany

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