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)

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
Keywords Second order arithmetic  Reverse mathematics  Real closed fields  Algebraically closed fields  Hilbert’s Nullstellensatz
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DOI 10.1007/s00153-003-0206-y
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Complex Analysis in Subsystems of Second Order Arithmetic.Keita Yokoyama - 2007 - Archive for Mathematical Logic 46 (1):15-35.

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