Distal and non-distal NIP theories
نویسندگان
چکیده
منابع مشابه
Distal and non-distal NIP theories
We study one way in which stable phenomena can exist in an NIP theory. We start by defining a notion of ‘pure instability’ that we call ‘distality’ in which no such phenomenon occurs. O-minimal theories and the p-adics for example are distal. Next, we try to understand what happens when distality fails. Given a type p over a sufficiently saturated model, we extract, in some sense, the stable pa...
متن کاملDistal and non-distal Pairs
The aim of this note is to determine whether certain non-o-minimal expansions of o-minimal theories which are known to be NIP, are also distal. We observe that while tame pairs of o-minimal structures and the real field with a discrete multiplicative subgroup have distal theories, dense pairs of o-minimal structures and related examples do not.
متن کاملDistal and Non-distal Behavior in Pairs
The aim of this work is an analysis of distal and non-distal behavior in dense pairs of o-minimal structures. A characterization of distal types is given through orthogonality to a generic type in Meq, non-distality is geometrically analyzed through Keisler measures, and a distal expansion for the case of pairs of ordered vector spaces is computed.
متن کاملType decomposition in NIP theories
A first order theory is NIP if all definable families of subsets have finite VCdimension. We provide a justification for the intuition that NIP structures should be a combination of stable and order-like components. More precisely, we prove that any type in an NIP theory can be decomposed into a stable part (a generically stable partial type) and an order-like quotient.
متن کاملA Guide to Nip Theories
INTRODUCTION This text is an introduction to the study of NIP (or dependent) theories. It is meant to serve two purposes. The first is to present various aspects of NIP theories and give the reader sufficient background material to understand the current research in the area. The second is to advertise the use of honest definitions, in particular in establishing basic results, such as the so-ca...
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: Annals of Pure and Applied Logic
سال: 2013
ISSN: 0168-0072
DOI: 10.1016/j.apal.2012.10.015