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On NIP and invariant measures

Ehud HrushovskiAnand Pillay — 2011

Journal of the European Mathematical Society

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 000 = G 00 for G definably amenable,...

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