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Abstract 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 -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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This content will become publicly available on July 15, 2025
Dynamical Control of Excitons in Atomically Thin Semiconductors
4. Eric L. Peterson, Trond I. Andersen, Giovanni Scuri, Andrew Y. Joe, Andrés M. Mier Valdivia, Xiaoling Liu, Alexander A. Zibrov, Bumho Kim, Takashi Taniguchi, Kenji Watanabe, James Hone, Valentin Walther, Hongkun Park, Philip Kim, Mikhail D. Lukin
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- Award ID(s):
- 2012023
- PAR ID:
- 10536061
- Publisher / Repository:
- arXiv
- Date Published:
- Journal Name:
- arXivorg
- ISSN:
- 2331-8422
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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