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 language | English (US) |
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Pages (from-to) | 35-44 |
Number of pages | 10 |
Journal | Results in Mathematics |
Volume | 45 |
Issue number | 1-2 |
DOIs | |
State | Published - Mar 1 2004 |
Keywords
- Lyndon’s preservation theorem
- affine geometry
- line-intersection
- positive definability
- projective geometry
ASJC Scopus subject areas
- Mathematics (miscellaneous)
- Applied Mathematics