Possible primitive notions for geometry of spine spaces

Abstract

New systems of notions specific to the geometry of spine spaces, are introduced. In particular parallelism turns out to be a sufficient primitive notion to express the geometry of a spine space, and we show that structures related to projective closure are definitionally equivalent to spine spaces.

Coplanarity of lines in projective and polar Grassmann spaces

“…Affine spaces, except those where all lines are of size 2, can be axiomatized by means of line intersection as a sole primitive notion [13]. In view of [29] binary line intersection is sufficient to express the geometry of spine spaces.…”