Transitivity of Kim-independence

Transitivity of Kim-independence

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 ▪-Morley sequences. We...

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Veröffentlicht in:Advances in mathematics (New York. 1965) 2021-03, Vol.379, p.107573, Article 107573
Hauptverfasser: Kaplan, Itay, Ramsey, Nicholas
Format: Artikel
Sprache:eng
Schlagworte:
Kim-independence
Model theory
NSOP1
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Zusammenfassung: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 ▪-Morley sequences. We give several applications, answering a number of open questions concerning transitivity, Morley sequences, and local character in NSOP1 theories.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2021.107573