Submission date: 18 September 2019

Abstract:

We study Kim-independence over arbitrary sets. Assuming that forking satisfies existence, we establish Kim's lemma for Kim-dividing over arbitrary sets in an NSOP_{1} theory. We deduce symmetry of Kim-independence and the independence theorem for Lascar strong types.

Mathematics Subject Classification:

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Full text arXiv 1909.08368: pdf, ps.