On the axiomatics of projective and affine geometry in terms of line intersection

Hans Havlicek, Victor Pambuccian

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

By providing explicit definitions, we show that in both affine and projective geometry of dimension >- 3, considered as first-order theories axiomatized in terms of lines as the only variables, nd the binary line-intersection predicate as primitive notion, non-intersection of two ines can be positively defined in terms of line-intersection.

Original languageEnglish (US)
Pages (from-to)35-44
Number of pages10
JournalResults in Mathematics
Volume45
Issue number1-2
DOIs
StatePublished - Mar 1 2004

Keywords

  • affine geometry
  • line-intersection
  • Lyndon’s preservation theorem
  • positive definability
  • projective geometry

ASJC Scopus subject areas

  • Mathematics (miscellaneous)
  • Applied Mathematics

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