Annals of Pure and Applied Logic 165 (2):695-723 (2014)

Abstract
We initiate a systematic study of the class of theories without the tree property of the second kind — NTP2. Most importantly, we show: the burden is “sub-multiplicative” in arbitrary theories ; NTP2 is equivalent to the generalized Kimʼs lemma and to the boundedness of ist-weight; the dp-rank of a type in an arbitrary theory is witnessed by mutually indiscernible sequences of realizations of the type, after adding some parameters — so the dp-rank of a 1-type in any theory is always witnessed by sequences of singletons; in NTP2 theories, simple types are co-simple, characterized by the co-independence theorem, and forking between the realizations of a simple type and arbitrary elements satisfies full symmetry; a Henselian valued field of characteristic is NTP2 if and only if the residue field is NTP2 , so in particular any ultraproduct of p-adics is NTP2; adding a generic predicate to a geometric NTP2 theory preserves NTP2
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DOI 10.1016/j.apal.2013.10.002
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References found in this work BETA

Generic Structures and Simple Theories.Z. Chatzidakis & A. Pillay - 1998 - Annals of Pure and Applied Logic 95 (1-3):71-92.
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.
Toward Classifying Unstable Theories.Saharon Shelah - 1996 - Annals of Pure and Applied Logic 80 (3):229-255.

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Citations of this work BETA

On Model-Theoretic Tree Properties.Artem Chernikov & Nicholas Ramsey - 2016 - Journal of Mathematical Logic 16 (2):1650009.
Generic Expansion and Skolemization in NSOP 1 Theories.Alex Kruckman & Nicholas Ramsey - 2018 - Annals of Pure and Applied Logic 169 (8):755-774.
Forking and Dividing in Henson Graphs.Gabriel Conant - 2017 - Notre Dame Journal of Formal Logic 58 (4):555-566.
Pseudo Real Closed Fields, Pseudo P-Adically Closed Fields and NTP2.Samaria Montenegro - 2017 - Annals of Pure and Applied Logic 168 (1):191-232.

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