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March 2006 Properties and consequences of Thorn-independence
Alf Onshuus
J. Symbolic Logic 71(1): 1-21 (March 2006). DOI: 10.2178/jsl/1140641160

Abstract

We develop a new notion of independence (þ-independence, read “thorn”-independence) that arises from a family of ranks suggested by Scanlon (þ-ranks). We prove that in a large class of theories (including simple theories and o-minimal theories) this notion has many of the properties needed for an adequate geometric structure.

We prove that þ-independence agrees with the usual independence notions in stable, supersimple and o-minimal theories. Furthermore, we give some evidence that the equivalence between forking and þ-forking in simple theories might be closely related to one of the main open conjectures in simplicity theory, the stable forking conjecture. In particular, we prove that in any simple theory where the stable forking conjecture holds, þ-independence and forking independence agree.

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Alf Onshuus. "Properties and consequences of Thorn-independence." J. Symbolic Logic 71 (1) 1 - 21, March 2006. https://doi.org/10.2178/jsl/1140641160

Information

Published: March 2006
First available in Project Euclid: 22 February 2006

zbMATH: 1103.03036
MathSciNet: MR2210053
Digital Object Identifier: 10.2178/jsl/1140641160

Rights: Copyright © 2006 Association for Symbolic Logic

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Vol.71 • No. 1 • March 2006
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