Résolution du problème de l'ellipse et du cercle par l'algorithme de Hörmander
Separating families for semi-algebraic sets.
Signatures et composantes connexes.
Some properties of the ring of Nash functions
Spaces of orderings of fields under finite extensions.
Splitting patterns of excellent quadratic forms.
Stability index of real varieties.
Summen n-ter Potenzen in Körpern.
Sums of 2 n-th Powers of Real Meromorphic Functions.
Sums of 2m-th powers of rational functions in one variable over real closed fields.
Sums of Fourth Powers of Real Algebraic Functions.
Sums of mixed powers in fields and orderings of prescribed level.
Sums of powers in rings and the real holomorphy ring.
Sums of Squares in Central Simple Algebras.
Sums of Squares in Division Algebras.
Sums of Squares of Linear Forms.
The absolute Galois group of a pseudo real closed field
The Boolean space of higher level orderings
Let K be an ordered field. The set X(K) of its orderings can be topologized to make it a Boolean space. Moreover, it has been shown by Craven that for any Boolean space Y there exists a field K such that X(K) is homeomorphic to Y. Becker's higher level ordering is a generalization of the usual concept of ordering. In a similar way to the case of ordinary orderings one can define a topology on the space of orderings of fixed exact level. We show that it need not be Boolean. However, our main theorem...
The Galois Cohomology of Pythagorean Fields.
The intersection theorem for orderings of higher level in rings.