Transitivity, lowness, and ranks in NSOP₁ theories

2020/06/18 by Artem Chernikov, Chernikov, Artem, Byunghan Kim +3 · 2 citations
Mathematics · #Advanced Operator Algebra Research #Advanced Topology and Set Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.2006.10486

openalex publication_date 2020/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop the theory of Kim-independence in the context of NSOP₁ theories satsifying the existence axiom. We show that, in such theories, Kim-independence is transitive and that \ind^K-Morley sequences witness Kim-dividing. As applications, we show that, under the assumption of existence, in a low NSOP₁ theory, Shelah strong types and Lascar strong types coincide and, additionally, we introduce a notion of rank for NSOP₁ theories.

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