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

Hans Havlicek; Victor Pambuccian

doi:10.1007/BF03322995

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

Hans Havlicek, Victor Pambuccian

Research output: Contribution to journal › Article › peer-review

10 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 language	English (US)
Pages (from-to)	35-44
Number of pages	10
Journal	Results in Mathematics
Volume	45
Issue number	1-2
DOIs	https://doi.org/10.1007/BF03322995
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

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10.1007/BF03322995

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title = "On the axiomatics of projective and affine geometry in terms of line intersection",

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.",

keywords = "Lyndon{\textquoteright}s preservation theorem, affine geometry, line-intersection, positive definability, projective geometry",

author = "Hans Havlicek and Victor Pambuccian",

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AU - Pambuccian, Victor

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N2 - 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.

AB - 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.

KW - Lyndon’s preservation theorem

KW - affine geometry

KW - line-intersection

KW - positive definability

KW - projective geometry

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

Abstract

Keywords

ASJC Scopus subject areas

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