Transitivity of Kim-independence
Logic
2020-12-08 v2
Abstract
We prove several results on the behavior of Kim-independence upon changing the base in NSOP theories. As a consequence, we prove that Kim-independence satisfies transitivity and that this characterizes NSOP. Moreover, we characterize witnesses to Kim-dividing as exactly the -Morley sequences. We give several applications, answering a number of open questions concerning transitivity, Morley sequences, and local character in NSOP theories.
Cite
@article{arxiv.1901.07026,
title = {Transitivity of Kim-independence},
author = {Itay Kaplan and Nicholas Ramsey},
journal= {arXiv preprint arXiv:1901.07026},
year = {2020}
}