Submission date: 10 July 2017

Abstract:

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}.

Mathematics Subject Classification:

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Full text arXiv 1707.02902: pdf, ps.