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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


Constructive Axiomatization of Plane Hyp
✍ Victor Pambuccian 📂 Article 📅 2001 🏛 John Wiley and Sons 🌐 English ⚖ 202 KB

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,

The complexity of plane hyperbolic incid
✍ Victor Pambuccian 📂 Article 📅 2005 🏛 John Wiley and Sons 🌐 English ⚖ 102 KB

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