Notre Dame Journal of Formal Logic

A Note on Generically Stable Measures and fsg Groups

Ehud Hrushovski, Anand Pillay, and Pierre Simon


We prove (Proposition 2.1) that if μ is a generically stable measure in an NIP (no independence property) theory, and μ(ϕ(x,b))=0 for all b, then for some n, μ(n)(y(ϕ(x1,y)ϕ(xn,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 , precisely as in stable groups, answering positively an earlier problem posed by the first two authors.

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Notre Dame J. Formal Logic, Volume 53, Number 4 (2012), 599-605.

First available in Project Euclid: 8 November 2012

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Zentralblatt MATH identifier

Primary: 03C45: Classification theory, stability and related concepts [See also 03C48]

Keisler measures NIP dependent fsg


Hrushovski, Ehud; Pillay, Anand; Simon, Pierre. A Note on Generically Stable Measures and fsg Groups. Notre Dame J. Formal Logic 53 (2012), no. 4, 599--605. doi:10.1215/00294527-1814705.

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