A continuous, constructive solution to Hilbert's 17th problem.
A note on linear preserves of ternary cubic forms
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...
A weak Hasse principle for central simple algebras with an involution.
An -algebra approach to Artin’s solution of Hilbert’s Seventeenth Problem
Using lattice-ordered algebras it is shown that a totally ordered field which has a unique total order and is dense in its real closure has the property that each of its positive semidefinite rational functions is a sum of squares.
Angeordnete affine Ebenen als Ebenen mit einem System von Halbgeraden, und euklidische Ebenen, die genau eine Anordnung besitzen.
Axiomatisations simples des theories des corps de rolle.
Bewertungen mit reeller Henselisierung.
Canonical ordering theorems, a first attempt
Central extensions of ordered skew fields.
Characterization of Fans and Hereditarily Pythagorean Fields.
Constructing Banaschewski compactification without Dedekind completeness axiom.
Coupures propres dans
Des automorphismes continus d'un corps de séries de Puiseux
Digressione sui campi ordinati
Embedding theorems for spaces of ℝ-places of rational function fields and their products
We study spaces M(R(y)) of ℝ-places of rational function fields R(y) in one variable. For extensions F|R of formally real fields, with R real closed and satisfying a natural condition, we find embeddings of M(R(y)) in M(F(y)) and prove uniqueness results. Further, we study embeddings of products of spaces of the form M(F(y)) in spaces of ℝ-places of rational function fields in several variables. Our results uncover rather unexpected obstacles to a positive solution of the open question whether the...
Erratum to "Fields of surreal numbers and exponentiation" (Fund. Math. 167 (2001), 173-188)
Estensioni di una struttura paracomplessa su un corpo algebricamente chiuso ad un suo ampliamento trascendente semplice
Fields: Algebraically closed and others.
Fields of surreal numbers and exponentiation
We show that Conway's field of surreal numbers with its natural exponential function has the same elementary properties as the exponential field of real numbers. We obtain ordinal bounds on the length of products, reciprocals, exponentials and logarithms of surreal numbers in terms of the lengths of their inputs. It follows that the set of surreal numbers of length less than a given ordinal is a subfield of the field of all surreal numbers if and only if this ordinal is an ε-number. In that case,...