On NIP and invariant measures

  • Anand Pillay

    University of Leeds, UK
  • Ehud Hrushovski

    Hebrew University, Jerusalem, Israel


We study forking, Lascar strong types, Keisler measures and definable groups, under an assumption of NIP (not the independence property), continuing aspects of the paper [16]. Among key results are (i) if does not fork over then the Lascar strong type of over coincides with the compact strong type of over and any global nonforking extension of is Borel definable over , (ii) analogous statements for Keisler measures and definable groups, including the fact that for definably amenable, (iii) definitions, characterizations and properties of “generically stable” types and groups, (iv) uniqueness of invariant (under the group action) Keisler measures on groups with finitely satisfiable generics, (v) a proof of the compact domination conjecture for (definably compact) commutative groups in -minimal expansions of real closed fields.

Cite this article

Anand Pillay, Ehud Hrushovski, On NIP and invariant measures. J. Eur. Math. Soc. 13 (2011), no. 4, pp. 1005–1061

DOI 10.4171/JEMS/274