The uniqueness of elementary embeddings

TL;DR

This paper investigates whether the structure of an inner model uniquely determines the elementary embedding of the universe of sets, a key question in the theory of large cardinals.

Contribution

It addresses the fundamental question of the uniqueness of elementary embeddings given an inner model, advancing understanding in large cardinal theory.

Findings

Provides conditions under which the embedding is unique

Identifies cases where non-uniqueness occurs

Contributes to the classification of elementary embeddings

Abstract

Much of the theory of large cardinals beyond a measurable cardinal concerns the structure of elementary embeddings of the universe of sets into inner models. This paper seeks to answer the question of whether the inner model uniquely determines the elementary embedding.