The elementary Archimedean axiom in absolute geometry

Research output: Contribution to journalArticle

Abstract

Absolute planes in which the elementary Archimedean axiom holds satisfy Aristotle’s axiom. Absolute planes satisfying both the elementary Archimedean axiom and Bachmann’s Lotschnittaxiom are Euclidean. The Corollary to Aristotle’s axiom is equivalent to Aristotle’s axiom.

Original languageEnglish (US)
Article number52
JournalJournal of Geometry
Volume110
Issue number3
DOIs
StatePublished - Dec 1 2019

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Keywords

  • Absolute plane geometry
  • Aristotle’s axiom
  • elementary Archimedean axiom
  • Euclidean parallel postulate
  • Lotschnittaxiom

ASJC Scopus subject areas

  • Geometry and Topology

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