The choiceless cardinals are inconsistent
Rupert McCallum
TL;DR
This paper proves the Kunen inconsistency within ZF set theory, demonstrating the non-existence of certain large cardinals.
Contribution
It provides a new proof of the Kunen inconsistency directly in ZF, without relying on the Axiom of Choice.
Findings
Kunen inconsistency holds in ZF
No nontrivial elementary embeddings of the universe exist in ZF
Strengthening the understanding of large cardinal limitations
Abstract
We give a proof of the Kunen inconsistency in ZF.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Computability, Logic, AI Algorithms · Mathematical and Theoretical Analysis