Notions of Independence in Model Theory

W. Hodges
Queen Mary and Westfield College, London

In the 1970s Saharon Shelah expanded the notion of a dependence relation by giving axioms for a 3-place relation `X is dependent on Y over Z'. His relation, under the name `forking', played a central role in understanding models of stable theories. Recent unpublished work of Hrushovski, Pillay and Kim has shown that Shelah's relation has useful properties in a much wider context.