Grassmann spaces of regular subspaces
Let \(\mathfrak{A}\) be a metric affine space and \(\mathfrak{P}\) be a metric projective space over a field \(F\) with \(\text{char}F\neq2\), where the metric is given by a bilinear form. A certain substructure of \(\mathfrak{A}\), respectively \(\mathfrak{P}\), is called a Grassmann space. The authors recover the original geometry from its Grassmann space. The investigations of the paper are parts of two (or even three) meta-geometrical problems: to characterize sufficient notions for a (geometrical) theory, to interpret one theory in another one, and to show axiomatizability of some class of structures.
scientific article; zbMATH DE number 5808435
scientific article