Transitivity of Kim-independence

Itay Kaplan; Nicholas Ramsey

doi:10.1016/j.aim.2021.107573

Transitivity of Kim-independence

Itay Kaplan, Nicholas Ramsey^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

8 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 language	English
Article number	107573
Journal	Advances in Mathematics
Volume	379
DOIs	https://doi.org/10.1016/j.aim.2021.107573
State	Published - 5 Mar 2021

Bibliographical note

Publisher Copyright:
© 2021

Keywords

Kim-independence
Model theory
NSOP

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10.1016/j.aim.2021.107573

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title = "Transitivity of Kim-independence",

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.",

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AB - 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.

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KW - Model theory

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Transitivity of Kim-independence

Abstract

Bibliographical note

Keywords

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