A Note on Generically Stable Measures and fsg Groups

作者：Hrushovski Ehud^*; Pillay Anand; Simon Pierre

来源：Notre Dame Journal of Formal Logic, 2012, 53(4): 599-605.

DOI：10.1215/00294527-1814705

• Keisler measures
• NIP
• dependent
• fsg

We prove (Proposition 2.1) that if mu is a generically stable measure in an NIP (no independence property) theory, and mu(phi(x, b)) = 0 for all b, then for some n, mu((n)) (there exists y(phi(x(1), y) Lambda center dot center dot center dot Lambda phi(X-n, y))) = 0. As a consequence we show (Proposition 3.2) that if G is a definable group with fsg (finitely satisfiable generics) in an NIP theory, and X is a definable subset of G, then X is generic if and only if every translate of X does not fork over empty set, precisely as in stable groups, answering positively an earlier problem posed by the first two authors.

• 出版日期2012