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In this paper we introduce a new invariant for extensions of difference fields, the , and discuss its properties.
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,...
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