The strong soundness theorem for real closed fields and Hilbert's Nullstellensatz in second order arithmetic
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\(_0\).
scientific article; zbMATH DE number 2123152