Simpler foundations for the hyperbolic plane

John Bamberg; Tim Penttila

doi:10.1515/forum-2022-0268

Simpler foundations for the hyperbolic plane

John Bamberg, Tim Penttila

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

H. L. Skala (1992) gave the first elegant first-order axiom system for hyperbolic geometry by replacing Menger's axiom involving projectivities with the theorems of Pappus and Desargues for the hyperbolic plane. In so doing, Skala showed that hyperbolic geometry is incidence geometry. We improve upon Skala's formulation by doing away with Pappus and Desargues altogether, by substituting for them two simpler axioms.

Original language	English
Pages (from-to)	1301-1325
Number of pages	25
Journal	Forum Mathematicum
Volume	35
Issue number	5
DOIs	https://doi.org/10.1515/forum-2022-0268
Publication status	Published - 1 Sept 2023

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10.1515/forum-2022-0268

https://arxiv.org/abs/2209.05933Licence: CC BY-ND

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Simpler foundations for the hyperbolic plane

Abstract

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Finite geometry from an algebraic point of view

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Simpler foundations for the hyperbolic plane

Abstract

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Finite geometry from an algebraic point of view

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