The axiomatics of ordered geometry: I. Ordered incidence spaces
The author presents a survey of the development of the axiomatic theory of ordered and half-ordered incidence geometry, starting from \textit{M. Pasch}'s book [Vorlesungen über neuere Geometrie. Leipzig. Teubner (1882; JFM 14.0498.01)]. For reasons of comparability, the different axiom systems are transferred into one common language, namely first-order logic. Only in the case of Archimedian ordered geometry extensions of first-order logic are needed. The paper contains a wealth of information, and it will certainly become a standard reference in the field. Particularly valuable is the bibliography which contains 358 entries and appears to be rather complete.
scientific article; zbMATH DE number 5882933
scientific article