Measurable cardinals and choiceless axioms
Gabriel Goldberg
TL;DR
This paper explores the relationship between large cardinal axioms and choiceless set theories, establishing that certain embeddings imply the existence of many measurable successor cardinals.
Contribution
It demonstrates that the existence of an elementary embedding from the universe to itself entails a proper class of measurable successor cardinals, linking large cardinals to choiceless axioms.
Findings
Existence of an elementary embedding implies many measurable successor cardinals.
Establishes a connection between large cardinal axioms and choiceless set theories.
Provides new insights into the structure of the set-theoretic universe.
Abstract
We prove that if there is an elementary embedding from the universe to itself, then there is a proper class of measurable successor cardinals.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Mathematical and Theoretical Analysis · Computability, Logic, AI Algorithms