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The axiomatics of ordered geometry: I. Ordered incidence spaces. (English) Zbl 1227.51010

The author presents a survey of the development of the axiomatic theory of ordered and half-ordered incidence geometry, starting from 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.

MSC:

51G05 Ordered geometries (ordered incidence structures, etc.)
01A60 History of mathematics in the 20th century
52A01 Axiomatic and generalized convexity
03B30 Foundations of classical theories (including reverse mathematics)

Citations:

JFM 14.0498.01
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Full Text: DOI

References:

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