Positive definitions of segment congruence in terms of segment inequality

• Autores: Victor Pambuccian
• Localización: Aequationes mathematicae, ISSN 0001-9054, Vol. 72, Nº. 3, 2006, págs. 243-253
• Idioma: inglés
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• Resumen

  • 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.