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

Archive for Mathematical Logic 43 (3):337-349 (2004)
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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

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Citations of this work

Complex analysis in subsystems of second order arithmetic.Keita Yokoyama - 2007 - Archive for Mathematical Logic 46 (1):15-35.

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References found in this work

Subsystems of Second Order Arithmetic.Stephen G. Simpson - 1999 - Studia Logica 77 (1):129-129.
Elements of mathematical logic.Georg Kreisel - 1967 - Amsterdam,: North Holland Pub. Co.. Edited by J. L. Krivine.
Countable algebra and set existence axioms.Harvey M. Friedman - 1983 - Annals of Pure and Applied Logic 25 (2):141.

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