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Algebraic characterization of isometries of the complex and the quaternionic hyperbolic planes

✍ Scribed by Wensheng Cao; Krishnendu Gongopadhyay


Book ID
113066056
Publisher
Springer
Year
2011
Tongue
English
Weight
242 KB
Volume
157
Category
Article
ISSN
0046-5755

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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