منابع مشابه
NIP for some pair-like theories
Generalising work from [2] and [6], we give sufficient conditions for a theory TP to inherit NIP from T , where TP is an expansion of the theory T by a unary predicate P . We apply our result to theories, studied in [1], of the real field with a subgroup of the unit circle.
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 کاملDistal 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 کاملWeight and Measure in NIP Theories
We initiate an account of Shelah’s notion of “strong dependence” in terms of generically stable measures, proving a measure analogue (for NIP theories) of the fact that a stable theory T is “strongly dependent” if and only if all (finitary) types have finite weight.
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ژورنال
عنوان ژورنال: Archive for Mathematical Logic
سال: 2010
ISSN: 0933-5846,1432-0665
DOI: 10.1007/s00153-010-0218-3