The higher sharp I: on $M_1^\#$

TL;DR

This paper explores the descriptive set theoretic representation of the mouse $M_1^{ ext{ extsterling}}$, specifically focusing on the case where n=1, contributing to the understanding of inner model theory.

Contribution

It provides a descriptive set theoretic characterization of the mouse $M_1^{ ext{ extsterling}}$, advancing the theoretical framework for analyzing such models.

Findings

Established the descriptive set theoretic representation of $M_1^{ ext{ extsterling}}$

Focused on the case n=1 in the hierarchy of mice

Contributed to the understanding of inner model theory and descriptive set theory

Abstract

We establish the descriptive set theoretic representation of the mouse $M_n^{\#}$, which is called $0^{(n+1)\#}$. This part deals with the case $n=1$.