Positive definitions of segment congruence in terms of segment inequality

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Abstract

It is shown that segment congruence can be defined by means of a positive existential definition in terms of segment inequality in several geometries over Archimedean ordered fields, and that it can be defined by means of a positive sentence in n-dimensional Euclidean geometry over arbitrary ordered fields.

Original languageEnglish (US)
Pages (from-to)243-253
Number of pages11
JournalAequationes Mathematicae
Volume72
Issue number3
DOIs
StatePublished - Dec 1 2006

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Keywords

  • Infinitary logic
  • Positive existential definability
  • Segment congruence
  • Segment inequality

ASJC Scopus subject areas

  • Mathematics(all)
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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