Critical embeddings
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866916081614979072 |
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| author | Karagila, Asaf Yuan, Jiachen |
| author_facet | Karagila, Asaf Yuan, Jiachen |
| contents | Hayut and 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 cardinals to not have any ultrapower elementary embeddings, as well as that it is consistent that no target model is closed. We also prove that if $κ$ is a critical point by any ultrapower embedding, then it is the critical point by a normal ultrapower embedding. The paper contains several open questions of interest in the study of critical cardinals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_02951 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Critical embeddings Karagila, Asaf Yuan, Jiachen Logic 03E55 (Primary), 03E25, 03E35 (Secondary) Hayut and 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 cardinals to not have any ultrapower elementary embeddings, as well as that it is consistent that no target model is closed. We also prove that if $κ$ is a critical point by any ultrapower embedding, then it is the critical point by a normal ultrapower embedding. The paper contains several open questions of interest in the study of critical cardinals. |
| title | Critical embeddings |
| topic | Logic 03E55 (Primary), 03E25, 03E35 (Secondary) |
| url | https://arxiv.org/abs/2401.02951 |