Abstract

We investigate certain aspects of the first-order theory of orthogonality structures - structures consisting of a domain of lines subject to a binary orthogonality relation. In particular, we establish definitions of various geometric and algebraic notions in terms of orthogonality, describe the construction of extremal subspaces using orthogonality, and show that the first-order theory of line orthogonality in the Euclidean n-space is not ℵ0-categorical for n ≥ 3