Abstract
M.Sc.
The geometric relation of orthogonality - when the angle determined by two lines is a
right angle - has a rich and interesting theory. We investigate geometric orthogonality
structures from a formal logical and model theoretic viewpoint, both using a domain
consisting of lines, where the orthogonality relation is a binary line relation, and also
using a domain consisting of points, where pairs of distinct points are treated as lines
and the orthogonality relation is treated as a quaternary relation on points. We establish
first-order axiom systems for these orthogonality structures for dimension n 2 2,
and examine some of the metamathematical properties of these structures and their
associated theories.