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 NSOP 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}
}