Transitivity of Kim-independence

Abstract

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