Maximal Prikry Sequences
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866914300325527552 |
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| author | Schimmerling, Ernest Zhang, Jiaming |
| author_facet | Schimmerling, Ernest Zhang, Jiaming |
| contents | In this paper we investigate the covering machinery of the Jensen-Steel core model $K$, under the hypothesis that there is no inner model with a Woodin cardinal. In an earlier work, Mitchell and the first author showed that if $ν>ω_2$ is a regular cardinal in $K$ but a singular ordinal in $V$, then $ν$ is a measurable cardinal in $K$. In this article, we further show that under certain circumstances, there exists a maximal Prikry sequence $C$ for a measure on $ν$ in $K$. The first author shows that the anti-large cardinal hypothesis is necessary. In a more restrictive setting, we prove that every subset of $ν$ with size $<|ν|$ can be covered by a set in $K[C]$ with size $<|ν|$. Benhamou and the first author show that the result is optimal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_22643 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Maximal Prikry Sequences Schimmerling, Ernest Zhang, Jiaming Logic In this paper we investigate the covering machinery of the Jensen-Steel core model $K$, under the hypothesis that there is no inner model with a Woodin cardinal. In an earlier work, Mitchell and the first author showed that if $ν>ω_2$ is a regular cardinal in $K$ but a singular ordinal in $V$, then $ν$ is a measurable cardinal in $K$. In this article, we further show that under certain circumstances, there exists a maximal Prikry sequence $C$ for a measure on $ν$ in $K$. The first author shows that the anti-large cardinal hypothesis is necessary. In a more restrictive setting, we prove that every subset of $ν$ with size $<|ν|$ can be covered by a set in $K[C]$ with size $<|ν|$. Benhamou and the first author show that the result is optimal. |
| title | Maximal Prikry Sequences |
| topic | Logic |
| url | https://arxiv.org/abs/2601.22643 |