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, and the binary line-intersection predicate as primitive notion, non-intersection of two lines can be positively defined in terms of line-intersection. (2000): 51A05, 51A15, 03C40, 03B30.
Mathematics Subject Classification