On NIP and invariant measures [article]

Ehud Hrushovski, Anand Pillay
2009 arXiv   pre-print
We study forking, Lascar strong types, Keisler measures and definable groups, under an assumption of NIP (not the independence property), continuing aspects of math.LO/0607442. 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
more » ... 0 = G^00 for G definably amenable, (iii) definitions, characterizations and properties of "generically stable" types and groups (iv) uniqueness of translation invariant Keisler measures on groups with finitely satisfiable generics (vi) A proof of the compact domination conjecture for definably compact commutative groups in o-minimal expansions of real closed fields.
arXiv:0710.2330v2 fatcat:xfsoqnaaazfajiw3ocn36dnll4