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Constructive Axiomatizations of Plane Absolute, Euclidean and Hyperbolic Geometry

✍ Scribed by Victor Pambuccian


Publisher
John Wiley and Sons
Year
2001
Tongue
English
Weight
154 KB
Volume
47
Category
Article
ISSN
0044-3050

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πŸ“œ SIMILAR VOLUMES


Constructive Axiomatization of Plane Hyp
✍ Victor Pambuccian πŸ“‚ Article πŸ“… 2001 πŸ› John Wiley and Sons 🌐 English βš– 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 πŸ“‚ Article πŸ“… 2005 πŸ› John Wiley and Sons 🌐 English βš– 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 βˆ€βˆƒβˆ€, but that there is an axiom system, all of whose axioms are βˆ€βˆƒβˆ€βˆƒ sentences. This remains true for Klingenberg's genera