Ternary Operations as Primitive Notions for Constructive Plane Geometry VI

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Abstract

In this paper we provide quantifier‐free, constructive axiomatizations for several fragments of plane Euclidean geometry over Euclidean fields, such that each axiom contains at most 4 variables. The languages in which they are expressed contain only at most ternary operations. In some precisely defined sense these axiomatizations are the simplest possible.

Original languageEnglish (US)
Pages (from-to)384-394
Number of pages11
JournalMathematical Logic Quarterly
Volume41
Issue number3
DOIs
StatePublished - 1995

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Keywords

  • Cartesian Plane
  • Constructive axiomatization
  • Euclidean Plane
  • Ordered Euclidean Plane
  • Plane Euclidean geometry

ASJC Scopus subject areas

  • Logic

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