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RANK-TO-RANK EMBEDDINGS AND STEEL’S CONJECTURE
Published online by Cambridge University Press: 13 November 2020
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.
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- © The Association for Symbolic Logic 2020