VC density of definable families over valued fields
نویسندگان
چکیده
We prove a tight bound on the number of realized 0=1 patterns (or equivalently Vapnik–Chervonenkis codensity) definable families in models theory algebraically closed valued fields with non-archimedean valuation. Our result improves best known this direction proved by Aschenbrenner, Dolich, Haskell, Macpherson and Starchenko, who weaker restricted case where characteristics field $K$ its residue are both assumed to be 0. The obtained here is optimal without any restriction characteristics. obtain aforementioned as consequence another bounding Betti numbers semi-algebraic subsets certain Berkovich analytic spaces, mirroring similar results already o-minimal structure for real well fields. latter first possibly independent interest. Its proof relies heavily recent Hrushovski Loeser topology spaces.
منابع مشابه
FUZZY HYPERVECTOR SPACES OVER VALUED FIELDS
In this note we first redefine the notion of a fuzzy hypervectorspace (see [1]) and then introduce some further concepts of fuzzy hypervectorspaces, such as fuzzy convex and balance fuzzy subsets in fuzzy hypervectorspaces over valued fields. Finally, we briefly discuss on the convex (balanced)hull of a given fuzzy set of a hypervector space.
متن کاملDefinable sets in algebraically closed valued fields: elimination of imaginaries
It is shown that if K is an algebraically closed valued field with valuation ring R, then Th(K) has elimination of imaginaries if sorts are added whose elements are certain cosets in K of certain definable R-submodules of K (for all n ≥ 1). The proof involves the development of a theory of independence for unary types, which play the role of 1-types, followed by an analysis of germs of definabl...
متن کاملOn Vc-density over Indiscernible Sequences
In this paper, we study VC-density over indiscernible sequences (denoted VCind-density). We answer an open question in [1], showing that VCind-density is always integer valued. We also show that VCind-density and dp-rank coincide in the natural way.
متن کاملfuzzy hypervector spaces over valued fields
in this note we first redefine the notion of a fuzzy hypervectorspace (see [1]) and then introduce some further concepts of fuzzy hypervectorspaces, such as fuzzy convex and balance fuzzy subsets in fuzzy hypervectorspaces over valued fields. finally, we briefly discuss on the convex (balanced)hull of a given fuzzy set of a hypervector space.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of the European Mathematical Society
سال: 2021
ISSN: ['1435-9855', '1435-9863']
DOI: https://doi.org/10.4171/jems/1056