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Differential Geometry of the Complex Plane

โœ Scribed by Julian Lowell Coolidge


Book ID
123784700
Publisher
American Mathematical Society
Year
1922
Tongue
English
Weight
908 KB
Volume
23
Category
Article
ISSN
0002-9947

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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