Transitives of betweenness

Transitives of betweenness
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Trans. Amer. Math. Soc. 52 (1942), 95-114

DOI: https://doi.org/10.1090/S0002-9947-1942-0007099-3

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References

Garrett Birkhoff, Lattice Theory, American Mathematical Society, New York, 1940. MR 0001959

Betweenness in metric ptolemaic spaces

Distance Geometries

W. D. Duthie, Segments of ordered sets, Trans. Amer. Math. Soc. 51 (1942), 1–14. MR 7032, DOI 10.1090/S0002-9947-1942-0007032-4
V. Glivenko, Contribution a L’Etude des Systemes de Choses Normees, Amer. J. Math. 59 (1937), no. 4, 941–956 (French). MR 1507294, DOI 10.2307/2371360

Géométrie des systèmes de choses normées

Edward V. Huntington, A new set of postulates for betweenness, with proof of complete independence, Trans. Amer. Math. Soc. 26 (1924), no. 2, 257–282. MR 1501278, DOI 10.1090/S0002-9947-1924-1501278-0
Edward V. Huntington and J. Robert Kline, Sets of independent postulates for betweenness, Trans. Amer. Math. Soc. 18 (1917), no. 3, 301–325. MR 1501071, DOI 10.1090/S0002-9947-1917-1501071-5
Karl Menger, Untersuchungen über allgemeine Metrik, Math. Ann. 100 (1928), no. 1, 75–163 (German). MR 1512479, DOI 10.1007/BF01448840

Grundlagen der Geometrie

Gilbert de B. Robinson, The Foundations of Geometry, Mathematical Expositions, No. 1, University of Toronto Press, Toronto, Ont., 1940. MR 0002929
I. J. Schoenberg, On metric arcs of vanishing Menger curvature, Ann. of Math. (2) 41 (1940), 715–726. MR 2903, DOI 10.2307/1968849

Axiomatik des Zwischenbegriffes in metrischen Räume

On the complete independence of the postulates for betweenness