Metrizable and $\mathbb {R}$-metrizable betweenness spaces
Juraj Šimko · Proceedings of the American Mathematical Society · 1999
It is proved that the theory of the class of all betweenness spaces metrizable by real-valued metrics does not coincide with the theory of the class of all betweenness spaces metrizable by metrics taking values in any ordered field. This solves a problem raised by Mendris and Zlatoš.