Notions around tree property 1

Annals of Pure and Applied Logic 162 (9):698-709 (2011)
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Abstract

In this paper, we study the notions related to tree property 1 , or, equivalently, SOP2. Among others, we supply a type-counting criterion for TP1 and show the equivalence of TP1 and k- TP1. Then we introduce the notions of weak k- TP1 for k≥2, and also supply type-counting criteria for those. We do not know whether weak k- TP1 implies TP1, but at least we prove that each weak k- TP1 implies SOP1. Our generalization of the tree-indiscernibility results in Džamonja and Shelah [5] is crucially used throughout the paper

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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.
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References found in this work

Simple theories.Byunghan Kim & Anand Pillay - 1997 - Annals of Pure and Applied Logic 88 (2-3):149-164.
Toward classifying unstable theories.Saharon Shelah - 1996 - Annals of Pure and Applied Logic 80 (3):229-255.
Characterizing Rosy Theories.Clifton Ealy & Alf Onshuus - 2007 - Journal of Symbolic Logic 72 (3):919 - 940.
On ◁∗-maximality.Mirna Džamonja & Saharon Shelah - 2004 - Annals of Pure and Applied Logic 125 (1-3):119-158.
Simplicity, and stability in there.Byunghan Kim - 2001 - Journal of Symbolic Logic 66 (2):822-836.

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