Transcendence degrees over mutually generic extensions
Fuente:
arXiv
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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908687656812544 |
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| author | Schilhan, Jonathan |
| author_facet | Schilhan, Jonathan |
| contents | Let $G_0$,..., $G_{n-1}$ be mutually generic over $V$, each $G_i$ adding at least one new real over $V$. We show that the transcendence degree of the reals of $V[G_0, \dots, G_{n-1}]$ is maximal (of size continuum) over the field generated by reals coming from models $V[ G_i : i \in a]$, for a proper subset $a$ of $n$. This answers a question of Fatalini and Schindler. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_02725 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Transcendence degrees over mutually generic extensions Schilhan, Jonathan Logic 03E40 Let $G_0$,..., $G_{n-1}$ be mutually generic over $V$, each $G_i$ adding at least one new real over $V$. We show that the transcendence degree of the reals of $V[G_0, \dots, G_{n-1}]$ is maximal (of size continuum) over the field generated by reals coming from models $V[ G_i : i \in a]$, for a proper subset $a$ of $n$. This answers a question of Fatalini and Schindler. |
| title | Transcendence degrees over mutually generic extensions |
| topic | Logic 03E40 |
| url | https://arxiv.org/abs/2512.02725 |