Transitivity of Kim-independence

Itay Kaplan, Nicholas Ramsey*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

We prove several results on the behavior of Kim-independence upon changing the base in NSOP1 theories. As a consequence, we prove that Kim-independence satisfies transitivity and that this characterizes NSOP1. Moreover, we characterize witnesses to Kim-dividing as exactly the [Formula presented]-Morley sequences. We give several applications, answering a number of open questions concerning transitivity, Morley sequences, and local character in NSOP1 theories.

Original languageAmerican English
Article number107573
JournalAdvances in Mathematics
Volume379
DOIs
StatePublished - 5 Mar 2021

Bibliographical note

Publisher Copyright:
© 2021

Keywords

  • Kim-independence
  • Model theory
  • NSOP

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