Reinhardt cardinals in inner models
Gabriel Goldberg
TL;DR
This paper explores the consistency of weakly Reinhardt and Reinhardt cardinals within second-order set theory without the Axiom of Choice, establishing their equiconsistency.
Contribution
It proves the equiconsistency of a proper class of weakly Reinhardt cardinals with a proper class of Reinhardt cardinals in a specific set-theoretic context.
Findings
Equiconsistency of weakly Reinhardt and Reinhardt cardinals
No reliance on the Axiom of Choice in the results
Advances understanding of large cardinals in second-order set theory
Abstract
A cardinal is weakly Reinhardt if it is the critical point of an elementary embedding from the universe of sets into a model that contains the double powerset of every ordinal. This note establishes the equiconsistency of a proper class of weakly Reinhardt cardinals with a proper class of Reinhardt cardinals in the context of second-order set theory without the Axiom of Choice.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Computability, Logic, AI Algorithms