English

On Kim-Independence

Logic 2019-01-09 v2

Abstract

We study NSOP1_{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 NSOP1_{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.

Cite

@article{arxiv.1702.03894,
  title  = {On Kim-Independence},
  author = {Itay Kaplan and Nicholas Ramsey},
  journal= {arXiv preprint arXiv:1702.03894},
  year   = {2019}
}
R2 v1 2026-06-22T18:17:10.569Z