Constructive rereading of Artin-Schreier theory

DOI10.1016/S0168-0072(97)80700-2zbMath0945.03094MaRDI QIDQ1382184

Henri Lombardi

Publication date: 8 October 2000

Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)

zbMATH Keywords

sums of squaresconstructive mathematicsreal closed fieldsordered fieldsHilbert's seventeenth problemdynamic evaluationreal fieldsArtin-Schreier theory

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) (12D15) Mechanization of proofs and logical operations (03B35) Effectivity, complexity and computational aspects of algebraic geometry (14Q20) Other constructive mathematics (03F65) Ordered fields (12J15)

Related Items (12)

THE JACOBSON RADICAL OF A PROPOSITIONAL THEORY ⋮ Eliminating disjunctions by disjunction elimination ⋮ Valuative Lattices and Spectra ⋮ ELIMINATING DISJUNCTIONS BY DISJUNCTION ELIMINATION ⋮ Valuative dimension, constructive points of view ⋮ A constructive comparison of the rings \(R(X)\) and \(R\langle X\rangle\) and application to the Lequain-Simis induction theorem ⋮ Hidden constructions in abstract algebra. VI: The theorem of Maroscia and Brewer {\&} Costa ⋮ Dynamical method in algebra: Effective Nullstellensätze ⋮ Hidden constructions in abstract algebra. I: Integral dependance. ⋮ Cut elimination for entailment relations ⋮ Construction of the Henselization of a valued field ⋮ Dynamical algebraic structures, pointfree topological spaces and Hilbert's program. (Structures algébriques dynamiques, espaces topologiques sans points et programme de Hilbert)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A course in constructive algebra
• Dynamic evaluation and real closure.
• A Nullstellensatz and a Positivstellensatz in semialgebraic geometry
• Sketches and computation – I: basic definitions and static evaluation
• Sketches and computation – II: dynamic evaluation and applications
• Dynamical method in algebra: Effective Nullstellensätze

This page was built for publication: Constructive rereading of Artin-Schreier theory