A continuous, constructive solution to Hilbert's 17th problem.
A note on involutory automorphisms of and the use of algebraically independent numbers for the construction of diagonable matrices
A note on the pp conjecture for sheaves of spaces of orderings
In this note we provide a direct and simple proof of a result previously obtained by Astier stating that the class of spaces of orderings for which the pp conjecture holds true is closed under sheaves over Boolean spaces.
A real nullstellensatz and positivstellensatz for the semipolynomials over an ordered field.
Let K be an ordered field and R its real closure. A semipolynomial will be defined as a function from Rn to R obtained by composition of polynomial functions and the absolute value. Every semipolynomial can be defined as a straight-line program containing only instructions with the following type: polynomial, absolute value, sup and inf and such a program will be called a semipolynomial expression. It will be proved, using the ordinary real positivstellensatz, a general real positivstellensatz concerning...
Abstract Grothendieck rings
Additive structure of multiplicative subgroups of fields and Galois theory.
Affine super-Pythagorean geometry.
Axiomatisations simples des theories des corps de rolle.
Central Orderings in Fields of Real Meromorphic Function Germs.
Chain signatures and real closures.
Characterization of Fans and Hereditarily Pythagorean Fields.
Constructing Quasi-Pythagorean Fields
Constructions de places réelles et géométrie semi-algébrique
Continous, piecewise-polynomial functions which solve Hilbert's 17th problem.
Decidable Theories of Preordered Fields.
Definite Lattices Over Real Algebraic Function Domains.
Die Stufe von Ordnungen ganzer Zahlen in algebraischen Zahlkörpern.
Dimensions of anisotropic indefinite quadratic forms. I.
Dimensions of anisotropic indefinite quadratic forms. II.
Divisionsalgebren über Funktionenkörpern