Rational points on algebraic varieties over a generalized real closed field: a model theoretic approach.
Real commutative algebra (I). Places.
Real commutative algebra (II). Plane curves.
Real commutative algebra. III. Dedekind-Weber-Riemann manifolds.
The space S of all non-trivial real places on a real function field K|k of trascendence degree one, endowed with a natural topology analogous to that of Dedekind and Weber's Riemann surface, is shown to be a one-dimensional k-analytic manifold, which is homeomorphic with every bounded non-singular real affine model of K|k. The ground field k is an arbitrary ordered, real-closed Cantor field (definition below). The function field K|k is thereby represented as a field of real mappings of S which might...
Rekursive Unentscheidbarkeit der Theorie der pythagoräischen Körper
Remarks on the Pythagoras and Hasse number of real fields.
Residual fields in valuation theory.
Residue class rings of real-analytic and entire functions
Let 𝓐(ℝ) and 𝓔(ℝ) denote respectively the ring of analytic and real entire functions in one variable. It is shown that if 𝔪 is a maximal ideal of 𝓐(ℝ), then 𝓐(ℝ)/𝔪 is isomorphic either to the reals or a real closed field that is an η₁-set, while if 𝔪 is a maximal ideal of 𝓔(ℝ), then 𝓔(ℝ)/𝔪 is isomorphic to one of the latter two fields or to the field of complex numbers. Moreover, we study the residue class rings of prime ideals of these rings and their Krull dimensions. Use is made of...
Résolution du problème de l'ellipse et du cercle par l'algorithme de Hörmander