Why are surjective lineations of the archimedean hyperbolic plane motions?

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Abstract

Positive ℒω1ω definitions of point-inequality and noncollinearity in terms of collinearity, which are valid in plane hyperbolic geometry over arbitrary Archimedean ordered Euclidean fields, provide a synthetic proof of the theorem stated in the title and first noticed to be a corollary of a result from by R. Höfer.

Original languageEnglish (US)
Pages (from-to)63-67
Number of pages5
JournalActa Mathematica Hungarica
Volume100
Issue number1-2
DOIs
StatePublished - Jul 1 2003

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Keywords

  • Definability
  • Hyperbolic geometry
  • ℒ-logic

ASJC Scopus subject areas

  • Mathematics(all)

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