Notions around tree property 1

作者：Kim Byunghan; Kim Hyeung Joon^*

来源：Annals of Pure and Applied Logic, 2011, 162(9): 698-709.

DOI：10.1016/j.apal.2011.02.001

• Tree property
• Fully tree indiscernible sequence

In this paper, we study the notions related to tree property 1 (=TP1), 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 Dzamonja and Shelah (2004)[5] is crucially used throughout the paper.

• 出版日期2011-9