A Logical Reading of the Nonexistence of Proper Homomorphisms Between Affine Spaces |
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Authors: | Victor Pambuccian |
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Affiliation: | (1) Department of Integrative Studies, Arizona State University West, PO Box 37100, Phoenix, AZ, 85069–7100, U.S.A. |
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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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Keywords: | affine geometry definability Lyndon's preservation theorem |
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