Simple Foundations for the Hyperbolic Plane
Logic
2022-09-14 v1 Combinatorics
Metric Geometry
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.
Keywords
Cite
@article{arxiv.2209.05933,
title = {Simple Foundations for the Hyperbolic Plane},
author = {John Bamberg and Tim Penttila},
journal= {arXiv preprint arXiv:2209.05933},
year = {2022}
}