The Ubiquitous Axiom

@article{Pambuccian2021TheUA,
  title={The Ubiquitous Axiom},
  author={Victor Pambuccian and Celia Schacht},
  journal={Results in Mathematics},
  year={2021},
  volume={76},
  pages={1-39}
}
This paper starts with a survey of what is known regarding an axiom, referred to as the Lotschnittaxiom, stating that the perpendiculars to the sides of a right angle intersect. Several statements are presented that turn out to rather unexpectedly be equivalent, with plane absolute geometry without the Archimedean axiom as a background, to the Lotschnittaxiom. One natural statement is shown to be strictly weaker than the Lotschnittaxiom, creating a chain of four statements, starting with the… 
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