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On the geometry, preemptions and complexity of

โœ Scribed by Evgeny V. Shchepin; Nodari Vakhania


Book ID
118297909
Publisher
Springer US
Year
2007
Tongue
English
Weight
601 KB
Volume
159
Category
Article
ISSN
0254-5330

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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 โˆ€โˆƒโˆ€, but that there is an axiom system, all of whose axioms are โˆ€โˆƒโˆ€โˆƒ sentences. This remains true for Klingenberg's genera