Linear and $\Bbb R$@-linear betweenness spaces

Rok, strany: 2001, 873 - 882

We will prove that the theory of the class of all betweenness spaces embeddable into some vector space over the reals does not coincide with the theory of the class of all betweenness spaces embeddable into some vector space over an arbitrary ordered field. This solves a problem raised by Mendris and Zlatoš in [Axiomatization and undecidability results for metrizable betweenness relations, Proc. Amer. Math. Soc. 123 (1995), 873–882].

ISO 690:

Šimko, J. 2001. Linear and $\Bbb R$@-linear betweenness spaces. In Mathematica Slovaca, vol. 51, no.4, pp. 873-882. 0139-9918.

APA:

Šimko, J. (2001). Linear and $\Bbb R$@-linear betweenness spaces. Mathematica Slovaca, 51(4), 873-882. 0139-9918.