# Sh:1118

• Kaplan, I., Ramsey, N., & Shelah, S. (2019). Local character of Kim-independence. Proc. Amer. Math. Soc., 147(4), 1719–1732.
• 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)
Bib entry
@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}
}