# Internal Categoricity and the Generic Multiverse

## TL;DR

This paper explores whether John Steel's generic multiverse theory is internally categorical, aiming to understand if the theory's subject matter is uniquely determined within its framework.

## Contribution

It investigates the internal categoricity of the generic multiverse theory, connecting forcing, categoricity, and the foundations of mathematics.

## Key findings

- MV may be internally categorical under certain conditions
- Internal categoricity arguments can shed light on the determinacy of the multiverse
- The results impact the understanding of mathematical foundations and multiverse theories

## Abstract

John Steel's theory, MV, of the generic multiverse provides a foundation for mathematics that aims to neutralize the effects of incompleteness brought on by forcing arguments. Jouko V\"a\"an\"anen's development of internal categoricity arguments provides opportunities to argue that the subject matter of some theory is, in some sense, determined. This paper investigates whether MV is internally categorical.