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Preprint Number 1160

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1160. Itay Kaplan, Nicholas Ramsey
On Kim-Independence

Submission date: 13 February 2017


We study NSOP_1 theories. We define Kim-independence, which generalizes non-forking independence in simple theories and corresponds to non-forking at a generic scale. We show that Kim-independence satisfies a version of Kim's lemma, local character, symmetry, and an independence theorem and that, moreover, these properties individually characterize NSOP_1 theories. We describe Kim-independence in several concrete theories and observe that it corresponds to previously studied notions of independence in Frobenius fields and vector spaces with a generic bilinear form.

Mathematics Subject Classification: 03C45, 03C55, 03C60

Keywords and phrases:

Full text arXiv 1702.03894: pdf, ps.

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