Submission date: 6 March 2007

Abstract:

A ternary relation between subsets of the big model of a complete first-order theory is called an independence relation if it satisfies a certain set of axioms. The primary example is forking in a simple theory, but o-minimal theories are also known to have an interesting independence relation. Our approach in this paper is to treat independence relations as mathematical objects worth studying. The main application is a better understanding of thorn-forking, which turns out to be closely related to modular pairs in the lattice of algebraically closed sets.

Mathematics Subject Classification: 03C45

Keywords and phrases: Independence relation, forking, thorn-forking

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