Local character of Kim-independence

2017/07/10 by Kaplan, Itay, Ramsey, Nicholas, Shelah, Saharon · 2 citations
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1707.02902

Abstract

We show that NSOP₁ theories are exactly the theories in which Kim-independence satisfies a form of local character. In particular, we show that if T is NSOP₁, M\models T, and p is a 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 NSOP₁. We also present a new phenomenon we call dual local-character for Kim-independence in NSOP₁-theories.

Cited by

• Abstract independence relations in neostability theory
• A note on stable Kim-forking

Related

• On Kim-Independence
• Transitivity of Kim-independence
• Independence over arbitrary sets in NSOP₁ theories
• Transitivity, lowness, and ranks in NSOP₁ theories
• Existence in NSOP₁ theories