Transversals in plane hyperbolic geometry
✍ Scribed by Knüppel, Frieder
- Book ID
- 125338232
- Publisher
- Springer
- Year
- 2013
- Tongue
- English
- Weight
- 236 KB
- Volume
- 105
- Category
- Article
- ISSN
- 0047-2468
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📜 SIMILAR VOLUMES
We provide a universal axiom system for plane hyperbolic geometry in a firstorder language with two sorts of individual variables, 'points' (upper-case) and 'lines' (lowercase), containing three individual constants, A0, A1, A2, standing for three non-collinear points, two binary operation symbols,
We show that plane hyperbolic geometry, expressed in terms of points and the ternary relation of collinearity alone, cannot be expressed by means of axioms of complexity at most ∀∃∀, but that there is an axiom system, all of whose axioms are ∀∃∀∃ sentences. This remains true for Klingenberg's genera