On a Class of Preorderrings of Higher Level.
Page 1 Next
Displaying 1 – 20 of 22
On convergence of integrals in o-minimal structures on archimedean real closed fields
Tobias Kaiser (2005)
Annales Polonici Mathematici
We define a notion of volume for sets definable in an o-minimal structure on an archimedean real closed field. We show that given a parametric family of continuous functions on the positive cone of an archimedean real closed field definable in an o-minimal structure, the set of parameters where the integral of the function converges is definable in the same structure.
On Finite Intersections of "Henselian Valued" Fields.
Bernhard Heinemann (1985)
Manuscripta mathematica
On full cover property of ordered fields
Tibor Šalát (1994)
Mathematica Slovaca
On preordered fields related to Hilbert's 17th problem.
Zeng Guangxin (1991)
Mathematische Zeitschrift
On Real Local-Global Principles.
Martin Krüskemper (1990)
Mathematische Zeitschrift
On Rings admitting orderings and 2-primary chains of orderings of higher level.
Eberhard Becker, Danielle Gondard (1989)
Manuscripta mathematica
On SAP Fields.
Werner Bäni, Herbert Gross (1978)
Mathematische Zeitschrift
On Sign Determinations in Real Algebraic Number Fields.
H. KEMPFERT (1968)
Numerische Mathematik
On Some Hasse Principles over Formally Real Fields.
Alexander Prestel, Richard Elman, Tsit-Yuen Lam (1973)
Mathematische Zeitschrift
On the class group of affinoid spaces
Elkedagmar Heinrich (1981/1982)
Groupe de travail d'analyse ultramétrique
On the dimension of the space of ℝ-places of certain rational function fields
Taras Banakh, Yaroslav Kholyavka, Oles Potyatynyk, Michał Machura, Katarzyna Kuhlmann (2014)
Open Mathematics
We prove that for every n ∈ ℕ the space M(K(x 1, …, x n) of ℝ-places of the field K(x 1, …, x n) of rational functions of n variables with coefficients in a totally Archimedean field K has the topological covering dimension dimM(K(x 1, …, x n)) ≤ n. For n = 2 the space M(K(x 1, x 2)) has covering and integral dimensions dimM(K(x 1, x 2)) = dimℤ M(K(x 1, x 2)) = 2 and the cohomological dimension dimG M(K(x 1, x 2)) = 1 for any Abelian 2-divisible coefficient group G.
On the Extension of Real Places
Manfred Knebusch (1973)
Commentarii mathematici Helvetici
On the seperation of basic semialgebraic sets by polynomials.
Ludwig Bröcker (1988)
Manuscripta mathematica
On the theory of cuts in ordered fields.
Pestov, G.G. (2001)
Sibirskij Matematicheskij Zhurnal
Ordered fields.
Francis RAYNER (1975/1976)
Seminaire de Théorie des Nombres de Bordeaux
Ordered fields and sign-changing polynomials.
T.M. Viswanathan (1977)
Journal für die reine und angewandte Mathematik
Ordered fields and the ultrafilter theorem
R. Berr, Françoise Delon, J. Schmid (1999)
Fundamenta Mathematicae
We prove that on the basis of ZF the ultrafilter theorem and the theorem of Artin-Schreier are equivalent. The latter says that every formally real field admits a total order.
Ordered Rings and Fields
Christoph Schwarzweller (2017)
Formalized Mathematics
We introduce ordered rings and fields following Artin-Schreier’s approach using positive cones. We show that such orderings coincide with total order relations and give examples of ordered (and non ordered) rings and fields. In particular we show that polynomial rings can be ordered in (at least) two different ways [8, 5, 4, 9]. This is the continuation of the development of algebraic hierarchy in Mizar [2, 3].
Ordering Epic R-Fields
Gábor Révész (1983)
Manuscripta mathematica
Currently displaying 1 – 20 of 22
Page 1 Next