Ternary Operations as Primitive Notions for Constructive Plane Geometry V

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10 Scopus citations


In this paper we provide a quantifier‐free, constructive axiomatization of metric‐Euclidean and of rectangular planes (generalizations of Euclidean planes). The languages in which the axiom systems are expressed contain three individual constants and two ternary operations. We also provide an axiom system in algorithmic logic for finite Euclidean planes, and for several minimal metric‐Euclidean planes. The axiom systems proposed will be used in a sequel to this paper to provide ‘the simplest possible’ axiom systems for several fragments of plane Euclidean geometry. Mathematics Subject Classification: 51M05, 51M15, 03F65.

Original languageEnglish (US)
Pages (from-to)455-477
Number of pages23
JournalMathematical Logic Quarterly
Issue number4
StatePublished - 1994


  • Algorithmic logic
  • Constructive axiomatization
  • Metric‐Euclidean planes
  • Rectangular planes

ASJC Scopus subject areas

  • Logic


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