On VC-Density in VC-Minimal Theories
نویسندگان
چکیده
We show that any formula with two free variables in a Vapnik–Chervonenkis (VC) minimal theory has VC-codensity at most 2. Modifying the argument slightly, we give new proof of fact that, VC-minimal where acleq= dcleq, is number (from work Aschenbrenner et al., author, and Laskowski).
منابع مشابه
Forking in VC-minimal theories
We consider VC-minimal theories admitting unpackable generating families, and show that in such theories, forking of formulae over a model M is equivalent to containment in global types definable over M , generalizing a result of Dolich on o-minimal theories in [4].
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 کاملOn VC-minimal fields and dp-smallness
In this paper, we show that VC-minimal ordered fields are real closed. We introduce a notion, strictly between convexly orderable and dp-minimal, that we call dp-small, and show that this is enough to characterize many algebraic theories. For example, dp-small ordered groups are abelian divisible and dp-small ordered fields are real closed.
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 کاملOn the Eeective Vc Dimension
The very idea of an \EEective Vapnik Chervonenkis (VC) dimension" (Vapnik, Levin and Le Cun, 1993) relies on the hypothesis that the relation between the generalization error and the number of training examples can be expressed by a formula algebraically similar to the VC bound. This hypothesis calls for a serious discussion since the traditional VC bound widely overestimates the generalization...
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: Notre Dame Journal of Formal Logic
سال: 2022
ISSN: ['0029-4527', '1939-0726']
DOI: https://doi.org/10.1215/00294527-2022-0019