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.
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Havlicek, H., Pambuccian, V. On the axiomatics of projective and affine geometry in terms of line intersection. Results. Math. 45, 35–44 (2004). https://doi.org/10.1007/BF03322995
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DOI: https://doi.org/10.1007/BF03322995