Generically stable types are stably dominated in C-minimal expansions of ACVF
نویسنده
چکیده
Let p(x) be a generically stable type over C0, thought of as a C0-definable type over U. The type p(x) might live in an imaginary sort. We are going to prove that there is a small set C ⊇ C0 and a C-definable map f into a power of k such that p is “dominated” over C by its pushforward along f . That is, for every D ⊇ C and every a, the following will be equivalent: • a |= p|D • a |= p|C and f(a) |= f∗p|D.
منابع مشابه
LIMIT AVERAGE SHADOWING AND DOMINATED SPLITTING
In this paper the notion of limit average shadowing property is introduced for diffeomorphisms on a compact smooth manifold M and a class of diffeomorphisms is given which has the limit average shadowing property, but does not have the shadowing property. Moreover, we prove that for a closed f-invariant set Lambda of a diffeomorphism f, if Lambda is C1-stably limit average shadowing and t...
متن کاملGeneric stability and stability
We prove two results about generically stable types p in arbitrary theories. The first, on existence of strong germs, generalizes results from [3] on stably dominated types. The second is an equivalence of forking and dividing, assuming generic stability of p for all m. We use the latter result to answer in full generality a question posed by Hasson and Onshuus: If p(x) ∈ S(B) is stable and doe...
متن کاملLifting stably dominated types
• Generic stability • Orthogonality to Γ • Stable domination. (In fact, after naming parameters, one gets domination by the generic type of k for some n.) Let X → Y be a definable surjection of interpretable sets. We will show that the induced map X̂ → Ŷ on the stable completions (space of generically stable types) is surjective. Using this, we can mimic the proof from Hrushovski and Loeser that...
متن کاملOn NIP and invariant measures
We study forking, Lascar strong types, Keisler measures and definable groups, under an assumption of NIP (not the independence property), continuing aspects of the paper [16]. Among key results are (i) if p = tp(b/A) does not fork over A then the Lascar strong type of b over A coincides with the compact strong type of b over A and any global nonforking extension of p is Borel definable over bdd...
متن کاملMinimal Types in Stable Banach Spaces
We prove existence of wide types in a continuous theory expanding a Banach space, and density of minimal wide types among stable types in such a theory. We show that every minimal wide stable type is “generically” isometric to an l2 space. We conclude with a proof of the following formulation of Henson’s Conjecture: every model of an uncountably categorical theory expanding a Banach space is pr...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2014