Abstract
A halfordered plane can be described in terms of a betweenness functiona on each of its lines, which fulfills the axiom of PASCH. For three different points of a line let Z be the number of the triplets (a,b,c), (b,c,a), (c,a,b) which have the value −1 relative toa. We will show that Z is either even or odd and that for Z=2 respectively Z=3 the halfordered plane is an affine plane of order 5 respectively 3. These results are generalizations of results of E. SPERNER ([7],[8]) and H. KARZEL ([2],[3]).
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Kreuzer, A. Klassifizierung von Halbordnungen. J Geom 33, 73–82 (1988). https://doi.org/10.1007/BF01230606
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DOI: https://doi.org/10.1007/BF01230606