# Derivatives of normal functions and omega-models

## TL;DR

This paper explores the relationship between the well-ordering principle for derivatives of normal functions on ordinals and the existence of large countable omega-models, establishing an equivalence between these concepts.

## Contribution

It demonstrates the equivalence between the well-ordering principle for derivatives of normal functions and the existence of arbitrarily large countable omega-models.

## Key findings

- Well-ordering principle for derivatives of normal functions is equivalent to the existence of large omega-models.
- Establishes a new connection between ordinal functions and model theory.
- Provides a foundational result in the theory of normal functions and models.

## Abstract

In this note the well-ordering principle for the derivative of normal functions on ordinals is shown to be equivalent to the existence of arbitrarily large countable coded omega-models of the well-ordering principle for the function.