Extendible cardinals and the mantle

TL;DR

This paper proves that the existence of an extendible cardinal implies the mantle is a ground model of the universe, linking large cardinal axioms to the structure of the set-theoretic universe.

Contribution

It establishes a new connection between extendible cardinals and the nature of the mantle as a ground model.

Findings

If an extendible cardinal exists, the mantle is a ground model.

The result connects large cardinal hypotheses with the structure of the universe.

Provides new insights into the relationship between large cardinals and set-theoretic geology.

Abstract

The mantle is the intersection of all ground models of $V$. We show that if there exists an extendible cardinal then the mantle is a ground model of $V$.