On NIP and invariant measures

Ehud Hrushovski, Anand Pillay
2011 Journal of the European Mathematical Society (Print)  
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 p = tp(b/A) does not fork over A then the Lascar strong type of b over A coincides with the compact strong type of b over A and any global nonforking extension of p is Borel definable over bdd(A), (ii) analogous statements for Keisler measures and definable groups, including the fact that G
more » ... 0 = G 00 for G 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 o-minimal expansions of real closed fields. E. Hrushovski: Hebrew University (Giv'at Ram),
doi:10.4171/jems/274 fatcat:peg6azkqwzh2nmisi5ireedruu