Thorn-forking as local forking

Journal of Mathematical Logic 9 (1):21-38 (2009)
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Abstract

A ternary relation [Formula: see text] between subsets of the big model of a complete first-order theory T 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.

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References found in this work

A geometric introduction to forking and thorn-forking.Hans Adler - 2009 - Journal of Mathematical Logic 9 (1):1-20.
Simplicity in compact abstract theories.Itay Ben-Yaacov - 2003 - Journal of Mathematical Logic 3 (02):163-191.
Properties and Consequences of Thorn-Independence.Alf Onshuus - 2006 - Journal of Symbolic Logic 71 (1):1 - 21.
Classification Theory and the Number of Nonisomorphic Models.S. Shelah - 1982 - Journal of Symbolic Logic 47 (3):694-696.
The number of types in simple theories.Enrique Casanovas - 1999 - Annals of Pure and Applied Logic 98 (1-3):69-86.

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