Forking in monadically NIP theories

@misc{chernikov2026forking,
  title = {{Forking in monadically NIP theories}},
  author = {Artem Chernikov},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.25068},
  eprint = {2609.25068},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.25068},
}

TY  - UNPB
TI  - Forking in monadically NIP theories
AU  - Artem Chernikov
PY  - 2026
DA  - 2026/09/17
PB  - arXiv
DO  - 10.48550/arxiv.2609.25068
UR  - https://arxiv.org/abs/2609.25068
AB  - We demonstrate that forking in monadically NIP theories satisfies a very strong form of triviality over arbitrary sets, generalizing Baldwin-Shelah in monadically stable theories and analogous to Shelah's result for finite satisfiability over models in monadically NIP theories. This implies in particular that strict non-forking independence is particularly well behaved, and that the forking relation induces a canonical semilinear partial order on singletons. We also give an example of an ω-categorical monadically NIP theory so that no finite set is an extension base.
ER  -