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A new proof of McKenna's theorem


Author: Guang Xin Zeng
Journal: Proc. Amer. Math. Soc. 102 (1988), 827-830
MSC: Primary 12D15
DOI: https://doi.org/10.1090/S0002-9939-1988-0934851-6
MathSciNet review: 934851
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Abstract: Using a new and simpler method, the following result is shown: Let $ (K,C)$ be a formally real field with core $ C$ which has only a finite number of orderings. Then $ (K,C)$ has the Weak Hilbert Property if and only if $ K$ is dense in every real closure of $ (K,C)$. This result contains the main theorem of McKenna in [1]


References [Enhancements On Off] (What's this?)

  • [1] K. McKenna, New facts about Hilbert's seventeenth problem, Lecture Notes in Math., vol. 498, Springer, 1975 pp. 220-230. MR 0401720 (53:5547)
  • [2] T. Y. Lam, The theory of ordered fields, Lecture Notes in Pure and Appl. Math., Vol. 55, Dekker, New York, 1980, pp. 1-152. MR 584611 (82e:12033)
  • [3] A. Prestel, Lectures on formally real fields, IMPA Lecture Notes, No. 22, Rio de Janeiro.
  • [4] -, Sums of squares over fields, Soc. Brasil Mat., Rio de Janeiro, 1979, pp. 33-44 MR82a: 12014. MR 572053 (82a:12014)
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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0934851-6
Keywords: Ordered fields, formally real fields with a core, the Weak Hilbert Property, definite rational functions
Article copyright: © Copyright 1988 American Mathematical Society

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