On generically stable types in dependent theories
نویسنده
چکیده
We develop the theory of generically stable types, independence relation based on nonforking and stable weight in the context of dependent (NIP) theories.
منابع مشابه
A Note on Morley Sequences in Dependent Theories
We characterize nonforking sequences in dependent (continuous and first order) theories in terms of a generalization of Poizat’s special sequences. We show that average types of Morley sequences are stationary over their domains and characterize generically stable types in terms of the structure of the “eventual” type.
متن کاملWeight and Measure in NIP Theories
We initiate an account of Shelah’s notion of “strong dependence” in terms of generically stable measures, proving a measure analogue (for NIP theories) of the fact that a stable theory T is “strongly dependent” if and only if all (finitary) types have finite weight.
متن کاملMorley Sequences in Dependent Theories
We characterize nonforking (Morley) sequences in dependent theories in terms of a generalization of Poizat’s special sequences and show that average types of Morley sequences are stationary over their domains. We characterize generically stable types in terms of the structure of the “eventual” type. We then study basic properties of “strict Morley sequences”, based on Shelah’s notion of strict ...
متن کاملGenerically 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....
متن کاملFinding generically stable measures
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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عنوان ژورنال:
- J. Symb. Log.
دوره 74 شماره
صفحات -
تاریخ انتشار 2009