Transitivity of Kim-independence

2019/01/21 by Kaplan, Itay, Ramsey, Nicholas · 1 citation
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1901.07026

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 \ind^K-Morley sequences. We give several applications, answering a number of open questions concerning transitivity, Morley sequences, and local character in NSOP₁ theories.

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• Abstract independence relations in neostability theory

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