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

Nobuyuki Sakamoto, Kazuyuki Tanaka

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

By RCA0, we denote a subsystem of second order arithmetic based on Δ10 comprehension and ∑1 0 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 RCA0.

Original languageEnglish
Pages (from-to)337-349
Number of pages13
JournalArchive for Mathematical Logic
Volume43
Issue number3
DOIs
Publication statusPublished - 2004 Apr 1

Keywords

  • Algebraically closed fields
  • Hilbert's Nullstellensatz
  • Real closed fields
  • Reverse mathematics
  • Second order arithmetic

ASJC Scopus subject areas

  • Philosophy
  • Logic

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