Zur Theorie der quadratischen Formen über formal reellen Körpern.
Eine Bemerkung zu den Wittringen endlicher Galoisscher Körpererweiterungen.
Characterization of Fans and Hereditarily Pythagorean Fields.
On the seperation of basic semialgebraic sets by polynomials.
Zur orthogonalen Geometrie über pythagoreischen Körpern.
On symmetric semialgebraic sets and orbit spaces
For a symmetric (= invariant under the action of a compact Lie group G) semialgebraic basic set C, described by s polynomial inequalities, we show, that C can also be written by s + 1 G-invariant polynomials. We also describe orbit spaces for the action of G by a number of inequalities only depending on the structure of G.
Reduction of semialgebraic constructible functions
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.
On the Mostowski Number.
Courbures intrinsèques dans les catégories analytico-géométriques
Deux types de courbures sont associés à un sous-ensemble compact et définissable d'une variété riemannienne analytique réelle. Si la variété est de courbure constante, il y a des relations linéaires entre ces mesures. Comme application, nous démontrons une formule cinématique, définissons des densités locales, et nous étudions les volumes des simplexes réguliers.
Valuations of function fields form the geometrical point of view.
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