Submission date: 21 January 2019

Abstract:

We prove several results on the behavior of Kim-independence upon changing the base in NSOP_{1} theories. As a consequence, we prove that Kim-independence satisfies transitivity and that this characterizes NSOP_{1}. Moreover, we characterize witnesses to Kim-dividing as exactly the \ind^{K}-Morley sequences. We give several applications, answering questions from our previous papers.

Mathematics Subject Classification:

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Full text arXiv 1901.07026 : pdf, ps.