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  • Author or Editor: V. Pambuccian x
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Abstract  

Positive Lω1ω definitions of point-inequality and noncollinearity in terms of collinearity, which are valid in plane hyperbolic geometry over arbitrary Archimedean ordered Euclidean fields, provide a synthetic proof of the theorem stated in the title and first noticed to be a corollary of a result from [2] by R. Höfer [3].

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Abstract  

We present an axiom system for plane hyperbolic geometry in a language with lines as the only individual variables and the binary relation of line-perpendicularity as the only primitive notion. It was made possible by results obtained by K. List and H.L. Skala. A similar axiomatization is possible for n-dimensional hyperbolic geometry with n≥4. We also point out that plane hyperbolic geometry admits a AE-axiomatization in terms of line-perpendicularity alone, an axiomatization we could not find.

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