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By introducing a new notion "local density", we show the fol- lowing result: Let (K, S) be a preordered field, then (K, S) has the weak Hubert 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.

A characterization of preordered fields with the weak Hilbert property