Subspaces and parallelity in semiaffine partial linear spaces (Q1429140)

The notion of semiaffine partial linear space was introduced by \textit{K. Radziszewski} [Zesz. Nauk., Geom. 19, 67--80 (1991; Zbl 0746.51003)]. The basic examples of these semiaffine partial linear spaces arise from cylinders over ruled quadrics, with generators of an arbitrary dimension. But there exist many other examples. The author studies in this article various properties of these semiaffine partial linear spaces. He characterizes subspaces and strong subspaces, considers the definability of projective and semiaffine planes, affine lines and parallelity in terms of projective lines. He also gives a construction of a wide class of semiaffine partial linear spaces.