2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/105076An axiomatic treatment of `independence relations' (notions of independence) for complete first-order theories is presented, the principal examples being forking (due to Shelah) and thorn-forking (due to Onshuus). Thorn-forking is characterised in terms of modular pairs in the lattice of algebraically closed sets. Wherever possible, forking and thorn-forking are treated in a uniform way. They are dual in the sense that forking is the finest (most restrictive) and thorn-forking the coarsest independence relation worth examining. We finish by defining the kernel of a sequence of indiscernibles and studying its relation to canonical bases.80 pages, 3 figures. Dissertation zur Erlangung des Doktorgrades der Fakultaet fuer Mathematik und Physik der Albert-Ludwigs-Universitaet Freiburg im Breisgau. Supervisor: Martin ZieglerLogic03C45 (Primary), 06C10 (Secondary)text