The strong soundness theorem for real closed fields and Hilbert's Nullstellensatz in second order arithmetic
type: Item
instance of: scholarly article
title: The strong soundness theorem for real closed fields and Hilbert's Nullstellensatz in second order arithmetic
zbMATH Open document ID: 1059.03069
author: Nobuyuki Sakamoto
author: Kazuyuki Tanaka
published in: Archive for Mathematical Logic
publication date: 2004-12-16T00:00:00Z
review text: The authors extend previous work by \textit{S. G. Simpson} and \textit{K. Tanaka} [Proceedings of the fourth Asian logic conference, Tokyo, 1990] and \textit{K. Tanaka} and \textit{T. Yamizaki} [in: S. G. Simpson (ed.), Reverse mathematics 2001 (to appear)], proving strong soundness theorems for satisfaction predicates for the reals and the complex numbers. Applying their results, they prove a version of Hilbert's Nullstellensatz for complex polynomials in RCA\(_0\).
reviewed by: Jeffry L. Hirst
Mathematics Subject Classification ID: 03F35
Mathematics Subject Classification ID: 12D10
zbMATH DE Number: 2123152
zbMATH Keywords: second-order arithmetic
zbMATH Keywords: reverse mathematics
zbMATH Keywords: real-closed fields
zbMATH Keywords: algebraically closed fields
zbMATH Keywords: Hilbert's Nullstellensatz
zbMATH Keywords: quantifier elimination
MaRDI profile type: Publication
full work available at URL: s00153-003-0206-y
OpenAlex ID: W2040234029
DOI: 10.1007/S00153-003-0206-Y
description: scientific article; zbMATH DE number 2123152