On Kim-independence

Itay Kaplan, Nicholas Ramsey

Research output: Contribution to journalArticlepeer-review

21 Scopus citations

Abstract

We study NSOP1 theories. We define Kim-independence, which generalizes non-forking independence in simple theories and corresponds to non-forking at a generic scale. We show that Kim-independence satisfies a version of Kim's lemma, local character, symmetry, and an independence theorem, and that moreover these properties individually characterize NSOP1 theories. We describe Kim-independence in several concrete theories and observe that it corresponds to previously studied notions of independence in Frobenius fields and vector spaces with a generic bilinear form.

Original languageAmerican English
Pages (from-to)1423-1474
Number of pages52
JournalJournal of the European Mathematical Society
Volume22
Issue number5
DOIs
StatePublished - 2020

Bibliographical note

Funding Information:
The first author would like to thank the Israel Science Foundation for partial support of this research (Grant no. 1533/14).

Publisher Copyright:
© European Mathematical Society 2020

Keywords

  • Kim-independence
  • NSOP
  • Simple theories

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