Remarks on NIP in a model

Abstract

We define the notion $\varphi (x,y)$ has $NIP$ in $A$, where $A$ is a subset of a model, and give some equivalences by translating results from [1]. Using additional material from [11] we discuss the number of coheirs when $A$ is not necessarily countable. We also revisit the notion "$\varphi (x,y)$ has $NOP$ in a model $M$" from [8].

This paper includes things from arXiv:1703.08731v2

Cited by in corpus (6)

• Dividing lines in unstable theories and subclasses of Baire 1 functions
• ${\aleph }_0$-categorical Banach spaces contain ${\ell }_p$ or $c_0$
• Galois groups as quotients of Polish groups
• Remarks on convergence of Morley sequences
• Generic Stability and Modes of Convergence
• Glivenko-Cantelli classes and NIP formulas