Abstract
We provide a collinearity based elementary axiomatics of optimal quantifier complexity ∀∃∀∃ for the geometry inside a triangle and reprove that collinearity cannot be defined in terms of segment congruence, the metric being Hilbert's projective metric.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 165-175 |
| Number of pages | 11 |
| Journal | Beitrage zur Algebra und Geometrie |
| Volume | 49 |
| Issue number | 1 |
| State | Published - Apr 7 2008 |
Keywords
- Collinearity
- Hilbert geometry inside a triangle
- Quantifier complexity
- Segment congruence
ASJC Scopus subject areas
- Algebra and Number Theory
- Geometry and Topology