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

DOI:
https://doi.org/10.1090/S0002-9939-1988-0962795-2

MathSciNet review:
962795

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Abstract | References | Similar Articles | Additional Information

Abstract: By introducing a new notion "local density", we show the following result: Let be a preordered field, then has the weak Hilbert property if and only if is locally dense. From this, a theorem of McKenna in reference [**1**] and one of Prestel in reference [**2**] will be easily proved.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1988-0962795-2

Keywords:
Preordered fields,
the weak Hilbert property,
definite rational functions,
local density

Article copyright:
© Copyright 1988
American Mathematical Society