No cardinal correct inner model elementarily embeds into the universe

TL;DR

This paper proves that no nontrivial cardinal-preserving elementary embedding from an inner model into the universe exists, resolving a question in set theory about the structure of inner models and their embeddings.

Contribution

It establishes the nonexistence of nontrivial cardinal-preserving elementary embeddings from inner models into the universe V.

Findings

No nontrivial cardinal-preserving elementary embedding from M into V exists.

Answers a previously open question by Caicedo.

Clarifies the structure of inner models and their elementary embeddings.

Abstract

An elementary embedding $j:M\rightarrow N$ between two inner models of ZFC is cardinal preserving if $M$ and $N$ correctly compute the class of cardinals. We look at the case $N=V$ and show that there is no nontrivial cardinal preserving elementary embedding from $M$ into $V$, answering a question of Caicedo.