Local character of Kim-independence

by Kaplan and Ramsey and Shelah. [KpRaSh:1118]

We show that NSOP_1 theories are exactly the theories in which Kim-independence satisfies a form of local character. In particular, we show that if T is NSOP_1, M models T, and p is a type over M, then the collection of elementary submodels of size |T| over which p does not Kim-fork is a club of [M]^{|T|} and that this characterizes NSOP_1 .


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