Generically stable and smooth measures in NIP theories
نویسندگان
چکیده
منابع مشابه
Generically stable and smooth measures in NIP theories
We formulate the measure analogue of generically stable types in first order theories with NIP (without the independence property), giving several characterizations, answering some questions from [9], and giving another treatment of uniqueness results from [9]. We introduce a notion of “generic compact domination”, relating it to stationarity of Keisler measures, and also giving group versions....
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This work builds on [6] and [7] where Keisler measures over NIP theories are studied. We discuss two constructions for obtaining generically stable measures in this context. First, we show how to symmetrize an arbitrary invariant measure to obtain a generically stable one from it. Next, we show that suitable sigma-additive probability measures give rise to generically stable Keisler measures. A...
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We develop the theory of generically stable types, independence relation based on nonforking and stable weight in the context of dependent (NIP) theories.
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Let M be an arbitrary structure. We say that an M -formula φ(x) defines a stable set in M if every formula φ(x)∧α(x, y) is stable. We prove: If G is an M -definable group and every definable stable subset of G has U-rank at most n (the same n for all sets) then G has a maximal connected stable normal subgroup H such that G/H is purely unstable. The assumptions holds for example when the structu...
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We prove (Proposition 2.1) that if μ is a generically stable measure in an NIP theory, and μ(φ(x, b)) = 0 for all b then for some n, μ(∃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 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 stab...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2012
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-2012-05626-1