Local character of kim-independence

Itay Kaplan, Nicholas Ramsey, Saharon Shelah

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

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 languageAmerican English
Pages (from-to)1719-1732
Number of pages14
JournalProceedings of the American Mathematical Society
Volume147
Issue number4
DOIs
StatePublished - 2018

Bibliographical note

Publisher Copyright:
© 2019 American Mathematical Society.

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