# Remarks on NIP in a model

## TL;DR

This paper explores the concept of NIP in models, providing equivalences, discussing coheirs in uncountable sets, and revisiting NOP, thereby deepening the theoretical understanding of model properties.

## Contribution

It introduces a formal definition of NIP in models, extends results to uncountable sets, and revisits the NOP notion, offering new theoretical insights.

## Key findings

- Established equivalences for NIP in models.
- Analyzed the number of coheirs in uncountable sets.
- Revisited and clarified the NOP concept in models.

## Abstract

We define the notion $\phi(x,y)$ 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 "$\phi(x,y)$ has $NOP$ in a model $M$" from [8].