Transitivity of Kim-independence
Abstract
We prove several results on the behavior of Kim-independence upon changing the base in NSOP$_{1}$ theories. As a consequence, we prove that Kim-independence satisfies transitivity and that this characterizes NSOP$_{1}$. Moreover, we characterize witnesses to Kim-dividing as exactly the $\ind^{K}$-Morley sequences. We give several applications, answering a number of open questions concerning transitivity, Morley sequences, and local character in NSOP$_{1}$ theories.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2019
- DOI:
- 10.48550/arXiv.1901.07026
- arXiv:
- arXiv:1901.07026
- Bibcode:
- 2019arXiv190107026K
- Keywords:
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- Mathematics - Logic