A logical reading of the nonexistence of proper homomorphisms between affine spaces (Q1580275)

In this short paper the author provides definitions of \(\neq\) and of non-collinearity 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' theorem stating that surjective maps between affine planes that preserve collinearity are isomorphisms, and of P. Maroscia's higher-dimensional generalization thereof.