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

  title={A note on stable sets, groups, and theories with NIP},
  author={Alf Onshuus and Ya'acov Peterzil},
  journal={Math. Log. Q.},
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

From This Paper

Topics from this paper.
2 Citations
10 References
Similar Papers


Publications citing this paper.


Publications referenced by this paper.
Showing 1-10 of 10 references

þ-forking in rosy theories, Ph.D

  • A. Onshuus
  • Thesis, University of California at Berkeley
  • 2002

Stable groups, Mathematical Surveys and Monographs 87

  • B. Poizat
  • American Mathematical Society,
  • 2001

Simple algebraic and semialgebraic groups over real closed fields

  • Y. Peterzil, Ya’acov, A. Pillay, S. Starchenko
  • Trans. Amer. Math. Soc.,
  • 2000

Stable groups, London Mathematical Society Lecture Note Series 240

  • F. Wagner
  • 1997

Geometric stability theory, Oxford Logic Guides 32

  • A. Pillay
  • 1996

Classification theory and the number of nonisomorphic models, Studies in Logic and the Foundations of Mathematics 92

  • S. Shelah
  • 1990

Similar Papers

Loading similar papers…