English

Independence over arbitrary sets in NSOP$_1$ theories

Logic 2019-09-19 v1

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 NSOP1_{1} theory. We deduce symmetry of Kim-independence and the independence theorem for Lascar strong types.

Cite

@article{arxiv.1909.08368,
  title  = {Independence over arbitrary sets in NSOP$_1$ theories},
  author = {Jan Dobrowolski and Byunghan Kim and Nicholas Ramsey},
  journal= {arXiv preprint arXiv:1909.08368},
  year   = {2019}
}
R2 v1 2026-06-23T11:19:03.273Z