No cardinal correct inner model elementarily embeds into the universe
Gabriel Goldberg, Sebastiano Thei

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 between two inner models of ZFC is cardinal preserving if and correctly compute the class of cardinals. We look at the case and show that there is no nontrivial cardinal preserving elementary embedding from into , answering a question of Caicedo.
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Taxonomy
TopicsCosmology and Gravitation Theories · Relativity and Gravitational Theory · Advanced Mathematical Theories
