Zur Unabhängigkeit von Hilberts Axiomen des affinen Raumes (Q1067599)

The aim of this article is to classify the incidence structures obtained in the following way: Assume that Hilbert's axioms, defining a classical affine space, are all satisfied except the uniqueness of the plane containing three given non-collinear points. Then, if the uniqueness of the plane is really not satisfied, such an incidence structure must be finite and, eliminating some entirely trivial variations, 39 models exist.