The strong soundness theorem for real closed fields and Hilbert's Nullstellensatz in second order arithmetic (Q701727)
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scientific article; zbMATH DE number 2123152
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The strong soundness theorem for real closed fields and Hilbert's Nullstellensatz in second order arithmetic |
scientific article; zbMATH DE number 2123152 |
Statements
The strong soundness theorem for real closed fields and Hilbert's Nullstellensatz in second order arithmetic (English)
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16 December 2004
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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\(_0\).
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second-order arithmetic
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reverse mathematics
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real-closed fields
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algebraically closed fields
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Hilbert's Nullstellensatz
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quantifier elimination
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