منابع مشابه
Stable embeddedness and NIP
We give some sufficient conditions for a predicate P in a complete theory T to be “stably embedded”. Let P be P with its “induced ∅definable structure”. The conditions are that P (or rather its theory) is “rosy”, P has NIP in T and that P is stably 1-embedded in T . This generalizes a recent result of Hasson and Onshuus [6] which deals with the case where P is o-minimal in T . Our proofs make u...
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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 apply the work of Bourgain, Fremlin and Talagrand on compact subsets of the first Baire class to show new results about φ-types for φ NIP. In particular, we show that if M is a countable model, then an M -invariant φ-type is Borel definable. Also the space of M invariant φ-types is a Rosenthal compactum, which implies a number of topological tameness properties. Shelah introduced the indepen...
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ژورنال
عنوان ژورنال: The Journal of Symbolic Logic
سال: 2011
ISSN: 0022-4812,1943-5886
DOI: 10.2178/jsl/1305810769