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2012 A Note on Generically Stable Measures and fsg Groups
Ehud Hrushovski, Anand Pillay, Pierre Simon
Notre Dame J. Formal Logic 53(4): 599-605 (2012). DOI: 10.1215/00294527-1814705

Abstract

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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Ehud Hrushovski. Anand Pillay. Pierre Simon. "A Note on Generically Stable Measures and fsg Groups." Notre Dame J. Formal Logic 53 (4) 599 - 605, 2012. https://doi.org/10.1215/00294527-1814705

Information

Published: 2012
First available in Project Euclid: 8 November 2012

zbMATH: 1318.03046
MathSciNet: MR2995423
Digital Object Identifier: 10.1215/00294527-1814705

Subjects:
Primary: 03C45

Rights: Copyright © 2012 University of Notre Dame

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Vol.53 • No. 4 • 2012
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