Weakly ordered plane geometry

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

A plane geometry is introduced, which although ordered such that both every line is densely linearly ordered without first or last element and such that every line partitions the points of the plane not incident with it into two convex half-planes, does not need to satisfy the Pasch axiom. An alternate axiomatization of ordered planes is obtained by adding several axioms, including the inner form of the Pasch axiom. The missing link between the inner form of Pasch's axiom and the full Pasch axiom is herewith determined.

Original languageEnglish (US)
Pages (from-to)91-96
Number of pages6
JournalAnnali dell'Universita di Ferrara
Volume56
Issue number1
DOIs
StatePublished - Feb 10 2010

Keywords

  • Inner form of the Pasch axiom
  • Plane ordered geometry
  • Weakly ordered plane

ASJC Scopus subject areas

  • Mathematics(all)

Fingerprint Dive into the research topics of 'Weakly ordered plane geometry'. Together they form a unique fingerprint.

Cite this