Sh:1118

• Kaplan, I., Ramsey, N., & Shelah, S. (2019). Local character of Kim-independence. Proc. Amer. Math. Soc., 147(4), 1719–1732. arXiv: 1707.02902 DOI: 10.1090/proc/14305 MR: 3910436
• Abstract:
  We show that NSOP$_1$ theories are exactly the theories in which Kim-independence satisfies a form of local character. In particular, we show that if $T$ is NSOP$_1$, $M \models T$, and $p$ is a type over $M$, then the collection of elementary submodels of size $|T|$ over which $p$ does not Kim-fork is a club of $[M]^{|T|}$ and that this characterizes NSOP$_1$.
• published version (14p)

@article{Sh:1118,
 author = {Kaplan, Itay and Ramsey, Nicholas and Shelah, Saharon},
 title = {{Local character of Kim-independence}},
 journal = {Proc. Amer. Math. Soc.},
 fjournal = {Proceedings of the American Mathematical Society},
 volume = {147},
 number = {4},
 year = {2019},
 pages = {1719--1732},
 issn = {0002-9939},
 mrnumber = {3910436},
 mrclass = {03C45 (03C55 03C80)},
 doi = {10.1090/proc/14305},
 note = {\href{https://arxiv.org/abs/1707.02902}{arXiv: 1707.02902}},
 arxiv_number = {1707.02902}
}