Notre Dame Journal of Formal Logic

A Note on Generically Stable Measures and fsg Groups

Ehud Hrushovski, Anand Pillay, and Pierre Simon

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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 $n$, $\mu^{(n)}(\exists y(\phi(x_{1},y)\wedge \cdots \wedge\phi(x_{n},y)))=0$. 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 $\emptyset$, 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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Mathematical Reviews number (MathSciNet)

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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  • [1] Conversano, A., and A. Pillay, “Connected components of definable groups and o-minimality, I,” Advances in Mathematics, vol. 231 (2012), pp. 605–23.
  • [2] Hrushovski, E., Y. Peterzil, and A. Pillay, “Groups, measures, and the $\mathit{NIP}$,” Journal of the American Mathematical Society, vol. 21 (2008), pp. 563–96.
  • [3] Hrushovski, E., and A. Pillay, “On $\mathit{NIP}$ and invariant measures,” Journal of the European Mathematical Society, vol. 13 (2011), pp. 1005–61.
  • [4] Hrushovski, E., A. Pillay, and P. Simon, “Generically stable and smooth measures in NIP theories,” to appear in Transactions of the American Mathematical Society.
  • [5] Newelski, L., “Model theoretic aspects of the Ellis semigroup,” Israel Journal of Mathematics, vol. 190 (2012), pp. 477–507.
  • [6] Pillay, A., “Weight and measure in $\mathit{NIP}$ theories,” to appear in Notre Dame Journal of Formal Logic.
  • [7] Pillay, A., and P. Tanovic, “Generic stability, regularity and quasiminimality,” pp. 189–211 in Models, Logics, and Higher-Dimensional Categories: A Tribute to the Work of Mihaly Makkai, edited by B. Mart, T. G. Kucera, A. Pillay, P. J. Scott, and R. A. G. Seely, vol. 53 of CRM Proceedings and Lecture Notes, American Mathematical Society, Providence, 2011.