  An 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.
