Elementary axiomatizations of projective space and of its associated grassmann space

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

It is pointed out that the axiomatizations of projective geometiy by means of point-line incidence, or by means of line-intersection, and that of the Grassmann space of the lines in a projective space are mutually translatable, so that one can obtain an axiomatization of any of these theories from the other, which in particular allows us to elementarily axiomatize the Grassmann space representing the lines of a projective space, a subject which has been extensively studied since 1981, when Tallini provided a non-elementary characterization for it.

Original languageEnglish (US)
Pages (from-to)129-144
Number of pages16
JournalNote di Matematica
Volume24
Issue number1
StatePublished - 2005

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Axiomatization
Projective Space
Line
Intersection of lines
Incidence

Keywords

  • First-order axiomatization
  • Grassmann space
  • Mutual interpretability
  • Projective geometry

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Elementary axiomatizations of projective space and of its associated grassmann space. / Pambuccian, Victor.

In: Note di Matematica, Vol. 24, No. 1, 2005, p. 129-144.

Research output: Contribution to journalArticle

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