A new proof of McKenna’s theorem

Zeng, Guang Xin

doi:10.1090/S0002-9939-1988-0934851-6

A new proof of McKenna’s theorem
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by Guang Xin Zeng

Proc. Amer. Math. Soc. 102 (1988), 827-830

DOI: https://doi.org/10.1090/S0002-9939-1988-0934851-6

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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

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T. Y. Lam, The theory of ordered fields, Ring theory and algebra, III (Proc. Third Conf., Univ. Oklahoma, Norman, Okla., 1979) Lecture Notes in Pure and Appl. Math., vol. 55, Dekker, New York, 1980, pp. 1–152. MR 584611

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