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arXiv · 2006.10486

Transitivity, lowness, and ranks in NSOP$_1$ theories

Artem Chernikov·Byunghan Kim·Nicholas Ramsey
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Abstract

We develop the theory of Kim-independence in the context of NSOP$_{1}$ 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 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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Artem Chernikov, Byunghan Kim, Nicholas Ramsey. 2020-06-18. Transitivity, lowness, and ranks in NSOP$_1$ theories. https://arxiv.org/abs/2006.10486

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