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A characterization of preordered fields with the weak Hilbert property

Author: Guangxin Zeng
Journal: Proc. Amer. Math. Soc. 104 (1988), 335-342
MSC: Primary 12D15; Secondary 11E25, 11E81, 12J15
MathSciNet review: 962795
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Abstract: By introducing a new notion "local density", we show the following result: Let $ (K,S)$ be a preordered field, then $ (K,S)$ has the weak Hilbert property if and only if $ (K,S)$ is locally dense. From this, a theorem of McKenna in reference [1] and one of Prestel in reference [2] will be easily proved.

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

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Keywords: Preordered fields, the weak Hilbert property, definite rational functions, local density
Article copyright: © Copyright 1988 American Mathematical Society

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