On Kim-Independence
Logic
2019-01-09 v2
Abstract
We study NSOP 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 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}
}