Local character of kim-independence

Itay Kaplan; Nicholas Ramsey; Saharon Shelah

doi:10.1090/proc/14305

Local character of kim-independence

Itay Kaplan, Nicholas Ramsey, Saharon Shelah

Einstein Institute of Mathematics

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

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Abstract

We show that NSOP ₁ theories are exactly the theories in which Kim-independence satisfies a form of local character. In particular, we show that if T is NSOP ₁ , M |= T, and p is a complete type over M, then the collection of elementary substructures of size |T | over which p does not Kim-fork is a club of [M] ^{|T |} and that this characterizes NSOP ₁ . We also present a new phenomenon we call dual local-character for Kim-independence in NSOP ₁ theories.

Original language	English
Pages (from-to)	1719-1732
Number of pages	14
Journal	Proceedings of the American Mathematical Society
Volume	147
Issue number	4
DOIs	https://doi.org/10.1090/proc/14305
State	Published - 2018

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© 2019 American Mathematical Society.

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Local character of kim-independence

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