English

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 NSOP1_{1} theories. As a consequence, we prove that Kim-independence satisfies transitivity and that this characterizes NSOP1_{1}. Moreover, we characterize witnesses to Kim-dividing as exactly the \indK\ind^{K}-Morley sequences. We give several applications, answering a number of open questions concerning transitivity, Morley sequences, and local character in NSOP1_{1} theories.

Keywords

Cite

@article{arxiv.1901.07026,
  title  = {Transitivity of Kim-independence},
  author = {Itay Kaplan and Nicholas Ramsey},
  journal= {arXiv preprint arXiv:1901.07026},
  year   = {2020}
}