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Preprint Number 1801

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1801. Artem Chernikov, Byunghan Kim, Nicholas Ramsey
Transitivity, lowness, and ranks in NSOP_1 theories

Submission date: 18 June 2020


We develop the theory of Kim-independence in the context of NSOP_1 theories satisfying the existence axiom. We show that, in such theories, Kim-independence is transitive and that ↓^K-Morley sequences witness Kim-dividing. As applications, we show that, under the assumption of existence, in a low NSOP_1 theory, Shelah strong types and Lascar strong types coincide and, additionally, we introduce a notion of rank for NSOP_1 theories.

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Full text arXiv 2006.10486: pdf, ps.

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