Explanation of Independence

Details Explanation of Independence Explanation of Independence

2005-11-24

arxiv.org/abs/math/0511616v1

Mathematics

Logic

80 pages, 3 figures. Dissertation zur Erlangung des Doktorgrades der Fakultaet fuer Mathematik und Physik der Albert-Ludwigs-U

Scientific paper

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.

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