Zur Abhängigkeit von Anordnungsaxiomen. (On relations between axioms of betweenness) (Q1100438)

Since the classical work of \textit{E. Sperner} [cp. Math. Ann. 121, 107-130 (1949; Zbl 0032.178)] the concept of order functions and betweenness functions has become a standard tool in the theory of ordered geometries. The author discusses the relations between various axioms of betweenness, including two versions of Pasch' axiom, in linear spaces. In particular, he gives some equivalent sets of axioms for halfordered and for ordered affine planes.