The core model induction beyond $L(\mathbb{R})$: non-tame mouse from PFA

TL;DR

This paper demonstrates that the Proper Forcing Axiom (PFA) implies the existence of a non-tame mouse, advancing the understanding of inner model theory and large cardinal hypotheses.

Contribution

It establishes a new connection between PFA and the existence of non-tame mice, extending core model induction beyond $L(\

Findings

PFA implies the existence of a non-tame mouse

Advances the core model induction techniques

Links forcing axioms with inner model theory

Abstract

We show that PFA implies that there is a non-tame mouse.