Abstract
We present an axiom system for plane hyperbolic geometry in a language with lines as the only individual variables and the binary relation of line-perpendicularity as the only primitive notion. It was made possible by results obtained by K. List [6] and H. L. Skala [15]. A similar axiomatization is possible for n-dimensional hyperbolic geometry with n ≧ 4. We also point out that plane hyperbolic geometry admits a ∀∃-axiomatization in terms of line-perpendicularity alone, an axiomatization we could not find.
Original language | English (US) |
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Pages (from-to) | 51-61 |
Number of pages | 11 |
Journal | Acta Mathematica Hungarica |
Volume | 101 |
Issue number | 1-2 |
DOIs | |
State | Published - Oct 1 2003 |
Keywords
- Hyperbolic geometry
- Line-orthogonality
ASJC Scopus subject areas
- General Mathematics