Witnessing Dp-Rank

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Notre Dame Journal of Formal Logic 55 (3):419-429 (2014)
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Abstract

We prove that in $\operatorname {NTP}_{\operatorname {2}}$ theories the dp-rank of a type can be witnessed by indiscernible sequences of tuples satisfying that type. If the type has dp-rank infinity, then this can be witnessed by singletons

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10.1215/00294527-2688105

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Citations of this work

Theories without the tree property of the second kind.Artem Chernikov - 2014 - Annals of Pure and Applied Logic 165 (2):695-723.
Dp-minimality: Invariant types and dp-rank.Pierre Simon - 2014 - Journal of Symbolic Logic 79 (4):1025-1045.
Exact saturation in simple and NIP theories.Itay Kaplan, Saharon Shelah & Pierre Simon - 2017 - Journal of Mathematical Logic 17 (1):1750001.
Non-forking and preservation of NIP and dp-rank.Pedro Andrés Estevan & Itay Kaplan - 2021 - Annals of Pure and Applied Logic 172 (6):102946.

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References found in this work

Theories without the tree property of the second kind.Artem Chernikov - 2014 - Annals of Pure and Applied Logic 165 (2):695-723.
Forking and dividing in NTP₂ theories.Artem Chernikov & Itay Kaplan - 2012 - Journal of Symbolic Logic 77 (1):1-20.
On dp-minimal ordered structures.Pierre Simon - 2011 - Journal of Symbolic Logic 76 (2):448 - 460.
On dp-minimality, strong dependence and weight.Alf Onshuus & Alexander Usvyatsov - 2011 - Journal of Symbolic Logic 76 (3):737 - 758.
On generically stable types in dependent theories.Alexander Usvyatsov - 2009 - Journal of Symbolic Logic 74 (1):216-250.

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