Abstract
It is pointed out that the axiomatizations of projective geometiy by means of point-line incidence, or by means of line-intersection, and that of the Grassmann space of the lines in a projective space are mutually translatable, so that one can obtain an axiomatization of any of these theories from the other, which in particular allows us to elementarily axiomatize the Grassmann space representing the lines of a projective space, a subject which has been extensively studied since 1981, when Tallini provided a non-elementary characterization for it.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 129-144 |
| Number of pages | 16 |
| Journal | Note di Matematica |
| Volume | 24 |
| Issue number | 1 |
| State | Published - Dec 1 2005 |
Keywords
- First-order axiomatization
- Grassmann space
- Mutual interpretability
- Projective geometry
ASJC Scopus subject areas
- General Mathematics