On VC-minimal fields and dp-smallness

نویسنده

  • Vincent Guingona
چکیده

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.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A Local Characterization of Vc-minimality

We show VC-minimality is Π4-complete. In particular, we give a local characterization of VC-minimality. We also show dp-smallness is Π1complete.

متن کامل

Convexly 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 کامل

On 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 کامل

Additivity of the Dp-rank

The main result is the prove of the linearity of the dp-rank. We also prove that the study of theories of finite dp-rank cannot be reduced to the study of its dp-minimal types and discuss the possible relations between dp-rank and VC-density.

متن کامل

Dp-Minimal Valued Fields

We show that dp-minimal valued fields are henselian and give classifications of dp-minimal ordered abelian groups and dp-minimal ordered fields without additional structure.

متن کامل

ذخیره در منابع من

ذخیره در منابع من قبلا به منابع من ذحیره شده

{@ msg_add @}


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:
  • Arch. Math. Log.

دوره 53  شماره 

صفحات  -

تاریخ انتشار 2014