A note on stable sets, groups, and theories with NIP

@article{Onshuus2007ANO,
  title={A note on stable sets, groups, and theories with NIP},
  author={Alf Onshuus and Ya'acov Peterzil},
  journal={Math. Log. Q.},
  year={2007},
  volume={53},
  pages={295-300}
}
Let M be an arbitrary structure. We say that an M -formula φ(x) defines a stable set in M if every formula φ(x)∧α(x, y) is stable. We prove: If G is an M -definable group and every definable stable subset of G has U-rank at most n (the same n for all sets) then G has a maximal connected stable normal subgroup H such that G/H is purely unstable. The assumptions holds for example when the structure M is interpretable in an o-minimal structure. More generally, an M -definable set X is called… CONTINUE READING

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