# Determined Admissible Sets

## TL;DR

Under hypotheses involving $^2$ Woodin cardinals, the paper proves the existence of a transitive model of KP + AD$_\mathbb{R}$ that includes all real numbers.

## Contribution

The paper establishes the existence of a specific model of set theory with determinacy assumptions under large cardinal hypotheses.

## Key findings

- Existence of a transitive model of KP + AD$_\mathbb{R}$ containing all reals.
- Results depend on hypotheses in the region of $^2$ Woodin cardinals.
- Advances understanding of models with determinacy and large cardinals.

## Abstract

It is shown, from hypotheses in the region of $\omega^2$ Woodin cardinals, that there is a transitive model of KP + AD$_\mathbb{R}$ containing all reals.

---
Source: https://tomesphere.com/paper/1907.00742