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RANK-TO-RANK EMBEDDINGS AND STEEL’S CONJECTURE

Part of: Set theory

Published online by Cambridge University Press:  13 November 2020

GABRIEL GOLDBERG
GABRIEL GOLDBERG*
Affiliation:
DEPARTMENT OF MATHEMATICS UC BERKELEYBERKELEY, CA94720, USAE-mail: ggoldberg@berkeley.edu
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Abstract

This paper establishes a conjecture of Steel [7] regarding the structure of elementary embeddings from a level of the cumulative hierarchy into itself. Steel’s question is related to the Mitchell order on these embeddings, studied in [5] and [7]. Although this order is known to be illfounded, Steel conjectured that it has certain large wellfounded suborders, which is what we establish. The proof relies on a simple and general analysis of the much broader class of extender embeddings and a variant of the Mitchell order called the internal relation.

Keywords

extenderMitchell orderinternal relationrank-to-rank

MSC classification

Primary: 03E55: Large cardinals
Type
Article
Information
The Journal of Symbolic Logic , Volume 86 , Issue 1 , March 2021 , pp. 137 - 147
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Copyright
© The Association for Symbolic Logic 2020

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References

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