A Logical Reading of the Nonexistence of Proper Homomorphisms between Affine Spaces

Victor Pambuccian

doi:10.1023/a:1005204912894

A Logical Reading of the Nonexistence of Proper Homomorphisms between Affine Spaces

Victor Pambuccian

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

4 Scopus citations

Abstract

We provide definitions of ≠ and of noncollinearity by positive statements in terms of the ternary predicate of collinearity which are valid in affine n-dimensional geometry. This provides the intrinsic reason for the validity of V. Corbas's theorem stating that surjective maps between affine planes that preserve collinearity are isomorphisms, and of P. Maroscia's higher-dimensional generalization thereof.

Original language	English (US)
Pages (from-to)	215-218
Number of pages	4
Journal	Geometriae Dedicata
Volume	81
Issue number	1-3
DOIs	https://doi.org/10.1023/a:1005204912894
State	Published - Jan 1 2000

Keywords

Affine geometry
Definability
Lyndon's preservation theorem

ASJC Scopus subject areas

Geometry and Topology

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10.1023/a:1005204912894

Cite this

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abstract = "We provide definitions of ≠ and of noncollinearity by positive statements in terms of the ternary predicate of collinearity which are valid in affine n-dimensional geometry. This provides the intrinsic reason for the validity of V. Corbas's theorem stating that surjective maps between affine planes that preserve collinearity are isomorphisms, and of P. Maroscia's higher-dimensional generalization thereof.",

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AB - We provide definitions of ≠ and of noncollinearity by positive statements in terms of the ternary predicate of collinearity which are valid in affine n-dimensional geometry. This provides the intrinsic reason for the validity of V. Corbas's theorem stating that surjective maps between affine planes that preserve collinearity are isomorphisms, and of P. Maroscia's higher-dimensional generalization thereof.

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KW - Definability

KW - Lyndon's preservation theorem

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A Logical Reading of the Nonexistence of Proper Homomorphisms between Affine Spaces

Abstract

Keywords

ASJC Scopus subject areas

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