A Local Characterization of Vc-minimality
نویسندگان
چکیده
We show VC-minimality is Π4-complete. In particular, we give a local characterization of VC-minimality. We also show dp-smallness is Π1complete.
منابع مشابه
Vc-minimality: Examples and Observations
VC-minimality is a recent notion in model theory which generalizes strong minimality, o-minimality, weak o-minimality and c-minimality, but is strong enough to imply various other properties of interest such as NIP and dp-minimality. In this paper, we answer several questions posed by Adler about the relationship of VC-minimality and older stability-theoretic notions in model theory. We also gi...
متن کاملOn VC-minimal theories and variants
In this paper, we study VC-minimal theories and explore related concepts. We first define the notion of convex orderablity and show that this lies strictly between VCminimality and dp-minimality. To do this we prove a general result about set systems with independence dimension ≤ 1. Next, we define the notion of weak VC-minimality, show it lies strictly between VC-minimality and dependence, and...
متن کاملConvexly orderable Groups and Valued Fields
We consider the model theoretic notion of convex orderability, which fits strictly between the notions of VC-minimality and dp-minimality. In some classes of algebraic theories, however, we show that convex orderability and VC-minimality are equivalent, and use this to give a complete classification of VC-minimal theories of ordered groups and abelian groups. Consequences for fields are also co...
متن کاملLocally o-minimal structures
In this paper we study (strongly) locally o-minimal structures. We first give a characterization of the strong local o-minimality. We also investigate locally o-minimal expansions of (R,+, <).
متن کاملHarmonicity and Minimality of Vector Fields on Lorentzian Lie Groups
We consider four-dimensional lie groups equipped with left-invariant Lorentzian Einstein metrics, and determine the harmonicity properties of vector fields on these spaces. In some cases, all these vector fields are critical points for the energy functional restricted to vector fields. We also classify vector fields defining harmonic maps, and calculate explicitly the energy of t...
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 2015