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The strong soundness theorem for real closed fields and Hilbert’s Nullstellensatz in second order arithmetic

The strong soundness theorem for real closed fields and Hilbert’s Nullstellensatz in second order... By RCA 0 , we denote a subsystem of second order arithmetic based on Δ0 1 comprehension and Δ0 1 induction. We show within this system that the real number system R satisfies all the theorems (possibly with non-standard length) of the theory of real closed fields under an appropriate truth definition. This enables us to develop linear algebra and polynomial ring theory over real and complex numbers, so that we particularly obtain Hilbert’s Nullstellensatz in RCA 0 . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Archive for Mathematical Logic Springer Journals

The strong soundness theorem for real closed fields and Hilbert’s Nullstellensatz in second order arithmetic

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References (11)

Publisher
Springer Journals
Copyright
Copyright © 2004 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics
ISSN
0933-5846
eISSN
1432-0665
DOI
10.1007/s00153-003-0206-y
Publisher site
See Article on Publisher Site

Abstract

By RCA 0 , we denote a subsystem of second order arithmetic based on Δ0 1 comprehension and Δ0 1 induction. We show within this system that the real number system R satisfies all the theorems (possibly with non-standard length) of the theory of real closed fields under an appropriate truth definition. This enables us to develop linear algebra and polynomial ring theory over real and complex numbers, so that we particularly obtain Hilbert’s Nullstellensatz in RCA 0 .

Journal

Archive for Mathematical LogicSpringer Journals

Published: Jan 15, 2004

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