I need to find an interprettion in which the incidence axioms and the first three betweeness axioms hold but the line separation property(Prop 3.4) fails. The hint is to pick a point P that is between A and B in the usual Euclidean sense and specify that A will now be considered to be between P and B. Leave all other betweeness realtions among points alone. Show that P lies neither on ray AB nor on its opposite ray AC