Homogeneity of linear spaces

Linear spaces are basic incidence structures consisting of points and lines, These are in fact first order structures naturally encoded by a single ternary relation. We shall discuss homogeneity questions, namely, when every small partial isomorphism extends to an automorphism. We show that the only non-degenerate homogeneous linear spaces are the two smallest projective planes.
Joint work with P. Nowakowski and T. Rzepecki.