Mathematics > Logic
[Submitted on 21 Jan 2019 (v1), last revised 5 Dec 2020 (this version, v2)]
Title:Transitivity of Kim-independence
View PDFAbstract: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.
Submission history
From: Nicholas Ramsey [view email][v1] Mon, 21 Jan 2019 18:32:06 UTC (27 KB)
[v2] Sat, 5 Dec 2020 03:57:55 UTC (30 KB)
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