Journal of Mathematical Logic 14 (2):1450008 (2014)

Abstract
We investigate the notions of strict independence and strict non-forking, and establish basic properties and connections between the two. In particular, it follows from our investigation that in resilient theories strict non-forking is symmetric. Based on this study, we develop notions of weight which characterize NTP2, dependence and strong dependence. Many of our proofs rely on careful analysis of sequences that witness dividing. We prove simple characterizations of such sequences in resilient theories, as well as of Morley sequences which are witnesses. As a by-product we obtain information on types co-dominated by generically stable types in dependent theories. For example, we prove that every Morley sequence in such a type is a witness.
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DOI 10.1142/s0219061314500081
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References found in this work BETA

A Geometric Introduction to Forking and Thorn-Forking.Hans Adler - 2009 - Journal of Mathematical Logic 9 (1):1-20.
On Dp-Minimal Ordered Structures.Pierre Simon - 2011 - Journal of Symbolic Logic 76 (2):448 - 460.
Forking and Dividing in NTP₂ Theories.Artem Chernikov & Itay Kaplan - 2012 - Journal of Symbolic Logic 77 (1):1-20.
On Dp-Minimality, Strong Dependence and Weight.Alf Onshuus & Alexander Usvyatsov - 2011 - Journal of Symbolic Logic 76 (3):737 - 758.
Classification Theory and the Number of Nonisomorphic Models.S. Shelah - 1982 - Journal of Symbolic Logic 47 (3):694-696.

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