Abstract
AbstractWe develop the theory of Kim-independence in the context of NSOP
$_{1}$
theories satisfying 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
$_{1}$
theory, Shelah strong types and Lascar strong types coincide and, additionally, we introduce a notion of rank for NSOP
$_{1}$
theories.
Publisher
Cambridge University Press (CUP)