Model theory and combinatorial pregeometries are tightly connected through the so called algebraic closure operator on strongly minimal sets. The research of projective and ane pregeometries are specifically fascinating since they have a close relation to vector spaces. In this dissertation we will see how the relationship happen and exactly how model theory can conclude a very strong classification theorem that divides pregeometries with certain properties into projective, and degenerate (trivial) cases.
Contents: Combinatorial geometries in model theory
3 Minimal sets
5 Algebraic closure
6 Incidence systems
7 The Trichotomy Theorem
8 Classiﬁcation theorem
Source: Uppsala University Library