Skip to main content
eScholarship
Open Access Publications from the University of California

External definability and groups in NIṔ theories

  • Author(s): Chernikov, A
  • Pillay, A
  • Simon, P
  • et al.
Abstract

We prove that many properties and invariants of definable groups in NIP theories (i.e. theories without the independence property), such as definable amenability, G/G^{00}, etc., are preserved when passing to the theory of the Shelah expansion by externally definable sets, M^{\operatorname {ext} }, of a model M. In the light of these results, we continue the study of the 'definable topological dynamics' of groups in \operatorname {NIP} theories. In particular, we prove the Ellis group conjecture relating the Ellis group to G/G^{00} in some new cases, including definably amenable groups in o-minimal structures. © 2014 London Mathematical Society.

Many UC-authored scholarly publications are freely available on this site because of the UC Academic Senate's Open Access Policy. Let us know how this access is important for you.

Main Content
Current View