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The complexity of plane hyperbolic incidence geometry is ∀∃∀∃

✍ Scribed by Victor Pambuccian

Publisher
John Wiley and Sons
Year
2005
Tongue
English
Weight
102 KB
Volume
51
Category
Article
ISSN
0044-3050

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✦ Synopsis

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 generalized hyperbolic planes, with arbitrary ordered fields as coordinate fields.

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