Critical embeddings

Asaf Karagila; Jiachen Yuan

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arXiv · 2401.02951

Critical embeddings

Asaf Karagila·Jiachen Yuan

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Abstract

Hayut and the first author isolated the notion of a critical cardinal in [1]. In this work, we answer several questions raised in the original paper. We show that it is consistent for a critical cardinal not to have any ultrapower elementary embeddings, as well as that it is consistent that no target model is closed. We also prove that if $\kappa$ is a critical point by any ultrapower embedding, then it is the critical point of an ultrapower embedding by a normal measure. The paper concludes by presenting several open questions of interest in the study of critical cardinals.

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BibTeX RIS

Asaf Karagila, Jiachen Yuan. 2024-01-05. Critical embeddings. https://arxiv.org/abs/2401.02951

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