The first measurable can be the first inaccessible cardinal
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915064403984384 |
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| author | Gitik, Moti Hayut, Yair Karagila, Asaf |
| author_facet | Gitik, Moti Hayut, Yair Karagila, Asaf |
| contents | In [8] the second and third authors showed that if the least inaccessible cardinal is the least measurable cardinal, then there is an inner model with $o(κ)\geq2$. In this paper we improve this to $o(κ)\geqκ+1$ and show that if $κ$ is a $κ^{++}$-supercompact cardinal, then there is a symmetric extension in which it is the least inaccessible and the least measurable cardinal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_02757 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The first measurable can be the first inaccessible cardinal Gitik, Moti Hayut, Yair Karagila, Asaf Logic Primary 03E25, Secondary 03E35, 03E55, 03E45 In [8] the second and third authors showed that if the least inaccessible cardinal is the least measurable cardinal, then there is an inner model with $o(κ)\geq2$. In this paper we improve this to $o(κ)\geqκ+1$ and show that if $κ$ is a $κ^{++}$-supercompact cardinal, then there is a symmetric extension in which it is the least inaccessible and the least measurable cardinal. |
| title | The first measurable can be the first inaccessible cardinal |
| topic | Logic Primary 03E25, Secondary 03E35, 03E55, 03E45 |
| url | https://arxiv.org/abs/2401.02757 |