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Preprint Number 93
93. Ehud Hrushovski and Anand Pillay
On NIP and invariant measures
Submission date: 19 October 2007.
We study forking, Lascar strong types, Keisler measures and definable groups, under an assumption of not the independence property. 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, (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) generic compact domination for groups with finitely satisfiable generics, (vi) (a proof of) the compact domination conjecture in the o-minimal case (i.e. for definably compact commutative groups in o-minimal expansions of real closed fields)
Mathematics Subject Classification: 03C60
Keywords and phrases: forking, the independence property, Keisler measure, o-minimal.
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