Transitivity, lowness, and ranks in NSOP$_1$ theories
Logic
2023-06-05 v2
Abstract
We develop the theory of Kim-independence in the context of NSOP theories satsifying the existence axiom. We show that, in such theories, Kim-independence is transitive and that -Morley sequences witness Kim-dividing. As applications, we show that, under the assumption of existence, in a low NSOP theory, Shelah strong types and Lascar strong types coincide and, additionally, we introduce a notion of rank for NSOP theories.
Cite
@article{arxiv.2006.10486,
title = {Transitivity, lowness, and ranks in NSOP$_1$ theories},
author = {Artem Chernikov and Byunghan Kim and Nicholas Ramsey},
journal= {arXiv preprint arXiv:2006.10486},
year = {2023}
}