On delta spaces satisfying Pasch's axiom
Connected partial linear spaces all of whose planes are projective are projective planes or Desarguesian projective spaces as follows by the classical result of Veblen and Young. The author has completely classified delta spaces containing only dual affine planes in the paper `Symplectic geometries, transvection groups and modules' (to appear in J. Comb. Theory, Ser. A) for the case that all lines have more than three points. The remaining cases have been classified by \textit{J. I. Hall} [Proc. Lond. Math. Soc., III. Ser. 58, No. 1, 89-111 (1989; Zbl 0673.20015)]. The main theorem of the present article with the result given above settles the classification of delta spaces in which all planes are projective or dual affine, up to the determination of projective and dual affine planes.
scientific article; zbMATH DE number 785147
scientific article